2013-05-19T04:12:07Z http://oai.repec.openlib.org/oai.php

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:505-5052010-11-09RePEc:oup:biomet

article 2 2005 92 June Biometrika 505 505 http://hdl.handle.net/10.1093/biomet/92.2.505 text/html Access to full text is restricted to subscribers. Albert W. Marshall Ingram Olkin

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:1025-1025a2010-11-09RePEc:oup:biomet

article The paper included comparison of a 12-factor, 16-run design to randomly generated Latin hypercube designs and U-designs, with respect to the properties of their alias matrices. An error in a computer program led to incorrect computation of the properties of the alias matrix of the orthogonal design. A corrected version of Table 2 is provided here. The orthogonal Latin hypercube design still has better properties than the best of 100 random designs, but the differences are less striking than those in our original table. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 1025 1025 http://hdl.handle.net/10.1093/biomet/93.4.1025-a text/html Access to full text is restricted to subscribers. David M. Steinberg Dennis K. J. Lin

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:219-2252010-11-09RePEc:oup:biomet

article We consider the problem of estimating a parameter theta, reflecting association between a disease and genotypes of a genetic polymorphism, using nuclear family data. In many applications, some parental genotypes are missing, and the distribution of these genotypes is unknown. Since misspecification of this distribution can bias estimators for theta, we consider estimating functions that are unbiased, regardless of how the distribution is specified. We call the resulting estimators parental-genotype-robust. Rabinowitz (2002) has proposed a constrained optimisation method for obtaining locally optimal unbiased tests of the null hypothesis of no association. We use a similar method to derive estimating functions that yield parental-genotype-robust estimators with minimum variance in the class of all such estimators. We extend the estimating functions to obtain parental-genotype-robust estimators when theta is a vector of unknown parameters, and show that the estimating functions enjoy a certain optimality property. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 219 225 Alice S. Whittemore

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:240-2452010-11-09RePEc:oup:biomet

article This paper studies properties of ordinary and generalised least squares estimators in a simple linear regression with stationary autocorrelated errors. Explicit expressions for the variances of the regression parameter estimators are derived for some common time series autocorrelation structures, including a first-order autoregression and general moving averages. Applications of the results include confidence intervals and an example where the variance of the trend slope estimator does not increase with increasing autocorrelation. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 240 245 Jaechoul Lee

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:1025-10252010-11-09RePEc:oup:biomet

article It has been brought to our attention that the implicit expression (6) for the estimator with general warping function had been derived earlier by B. Ronn, in an unpublished technical report of the Royal Veterinary and Agricultural University, Frederiksberg. However, the actual implementation and computation of the estimators are very different in our paper from in the technical report. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 1025 1025 http://hdl.handle.net/10.1093/biomet/93.4.1025 text/html Access to full text is restricted to subscribers. D. Gervini T. Gasser

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:177-1932010-11-09RePEc:oup:biomet

article For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within-cluster correlation. We show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly unrelated kernel estimator of Wang (2003) for any working covariance matrix. We show that both estimators can be obtained iteratively by applying conventional kernel or spline smoothing to pseudo-observations. This result allows us to study the asymptotic properties of the smoothing spline estimator by deriving its asymptotic bias and variance. We show that smoothing splines are consistent for an arbitrary working covariance and have the smallest variance when assuming the true covariance. We further show that both the seemingly unrelated kernel estimator and the smoothing spline estimator are nonlocal unless working independence is assumed but have asymptotically negligible bias. Their finite sample performance is compared through simulations. Our results justify the use of efficient, non-local estimators such as smoothing splines for clustered/longitudinal data. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 177 193 Xihong Lin

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:505-505a2010-11-09RePEc:oup:biomet

article 2 2005 92 June Biometrika 505 505 http://hdl.handle.net/10.1093/biomet/92.2.505-a text/html Access to full text is restricted to subscribers. Shaun R. Seaman Sylvia Richardson

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:525-5362009-04-05RePEc:oup:biomet

article In this paper we evaluate the characteristics observed both on a crime sample and on individuals included in a database to assess the probability of alternative hypotheses concerning identification. The problem is first addressed by considering a generic characteristic and we demonstrate the problem via a computationally efficient Bayesian network. Then we turn our attention to a heritable DNA trait to show how to evaluate the hypotheses that some individuals, genetically related to the members of the database, are the donors of the crime sample. Then the network is extended to cope with many loci. Applications of the method are provided as well as details of computational requirements. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 525 536 http://hdl.handle.net/10.1093/biomet/93.3.525 text/html Access to full text is restricted to subscribers. David Cavallini Fabio Corradi

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:991-9942009-04-05RePEc:oup:biomet

article In a recent paper, Lo et al. (2001) propose a test for the likelihood ratio statistic based on the Kullback--Leibler information criterion when testing the null hypothesis that a random sample is drawn from a mixture of k-sub-0 normal components against the alternative hypothesis of a mixture with k-sub-1 normal components with k-sub-0 less than k-sub-1. However, this result requires conditions that are generally not met when the null hypothesis holds. Consequently, the result is not proven and simulations suggest that it may not be correct. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 991 994 Neal O. Jeffries

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:235-2542009-04-05RePEc:oup:biomet

article An important problem in shape analysis is to match configurations of points in space after filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are either unlabelled or have at most a partial labelling constraining the matching, and in which some points may only appear in one of the configurations. We derive procedures for simultaneous inference about the matching and the transformation, using a Bayesian approach. Our hierarchical model is based on a Poisson process for hidden true point locations; this leads to considerable mathematical simplification and efficiency of implementation of <EM t="s">EM and Markov chain Monte Carlo algorithms. We find a novel use for classical distributions from directional statistics in a conditionally conjugate specification for the case where the geometrical transformation includes an unknown rotation. Throughout, we focus on the case of affine or rigid motion transformations. Under a broad parametric family of loss functions, an optimal Bayesian point estimate of the matching matrix can be constructed that depends only on a single parameter of the family. Our methods are illustrated by two applications from bioinformatics. The first problem is of matching protein gels in two dimensions, and the second consists of aligning active sites of proteins in three dimensions. In the latter case, we also use information related to the grouping of the amino acids, as an example of a more general capability of our methodology to include partial labelling information. We discuss some open problems and suggest directions for future work. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 235 254 http://hdl.handle.net/10.1093/biomet/93.2.235 text/html Access to full text is restricted to subscribers. Peter J. Green Kanti V. Mardia

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:669-6822009-04-05RePEc:oup:biomet

article Suppose a population has infinitely many individuals and is partitioned into unknown N disjoint classes. The sample coverage of a random sample from the population is the total proportion of the classes observed in the sample. This paper uses a nonparametric Poisson mixture model to give new understanding and results for inference on the sample coverage. The Poisson mixture model provides a simplified framework for inferring any general abundance-K coverage, the sum of the proportions of those classes that contribute exactly k individuals in the sample for some k in K, with K being a set of nonnegative integers. A new moment-based derivation of the well-known Turing estimators is presented. As an application, a gene-categorisation problem in genomic research is addressed. Since Turing's approach is a moment-based method, maximum likelihood estimation and minimum distance estimation are indicated as alternatives for the coverage problem. Finally, it will be shown that any Turing estimator is asymptotically fully efficient. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 669 682 Chang Xuan Mao

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:591-6022009-04-05RePEc:oup:biomet

article A multivariate Gaussian graphical Markov model for an undirected graph G, also called a covariance selection model or concentration graph model, is defined in terms of the Markov properties, i.e. conditional independences associated with G, which in turn are equivalent to specified zeros among the set of pairwise partial correlation coefficients. By means of Fisher's z-transformation and Šidák's correlation inequality, conservative simultaneous confidence intervals for the entire set of partial correlations can be obtained, leading to a simple method for model selection that controls the overall error rate for incorrect edge inclusion. The simultaneous p-values corresponding to the partial correlations are partitioned into three disjoint sets, a significant set S, an indeterminate set I and a nonsignificant set N. Our model selection method selects two graphs, a graph &Gcirc;-sub-SI whose edges correspond to the set S∪I, and a more conservative graph &Gcirc;-sub-S whose edges correspond to S only. Similar considerations apply to covariance graph models, which are defined in terms of marginal independence rather than conditional independence. The method is applied to some well-known examples and to simulated data. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 591 602 Mathias Drton

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:367-3832009-04-05RePEc:oup:biomet

article Nonparametric estimators for competing risks data can be applied to semicompeting risks data, a type of multi-state data where a terminating event may censor a nonterminating event, after forcing the data into the competing risks format. Complications may arise with left truncation of the terminating event, where the competing risks analysis naively truncates the nonterminating event using the left-truncation time for the terminating event, which may lead to large efficiency losses. We propose nonparametric estimators which use all semicompeting risks information and do not require artificial truncation. The uniform consistency and weak convergence of the estimators are established and variance estimators are provided. Simulation studies and an analysis of a diabetes registry demonstrate large efficiency gains over the naive estimators. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 367 383 http://hdl.handle.net/10.1093/biomet/93.2.367 text/html Access to full text is restricted to subscribers. L. Peng J. P. Fine

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:239-2442009-04-05RePEc:oup:biomet

article We exploit a reparameterisation of the marginal covariance matrix arising in longitudinal studies (Pourahmadi, 1999, 2000) to model, jointly, the mean and covariance structures in terms of three polynomial functions of time. By reanalysing Kenward's (1987) cattle data, we compare model selection procedures based on regressogram estimation with these based on a global search of the model space. Using a BIC-based model selection criterion to identify the optimum degree triple of the three polynomials, we show that the use of a saturated mean model is not optimal and explain why regressogram-based model estimation may be misleading. We also suggest a new computational method for finding the global optimum based on a criterion involving three pairwise saturated profile likelihoods. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 239 244 Jianxin Pan

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:423-4342009-04-05RePEc:oup:biomet

article In this paper we consider optimal design of experiments in the case of correlated observations. We use and further develop the concept of design measures introduced by Pázman & Müller (1998) for the construction of a simple, quick and elegant design algorithm. We support the construction of this algorithm for a general correlation structure by an interpretation in terms of norms. Examples demonstrate that our results are useful for generating exact designs by sampling from the obtained design measures. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 423 434 Werner G. Müller

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:1006-10082009-04-05RePEc:oup:biomet

article Nonparametric quantile inference for competing risks has recently been studied by Peng & Fine (2007). Their key result establishes uniform consistency and weak convergence of the inverse of the Aalen--Johansen estimator of the cumulative incidence function, using the representation of the cumulative incidence estimator as a sum of independent and identically distributed random variables. The limit process is of a form similar to that of the standard survival result, but with the cause-specific hazard of interest replacing the all-causes hazard. We show that this fact is not a coincidence, but can be derived from a general Hadamard differentiation result. We discuss a simplified proof and extensions of the approach to more complex multistate models. As a further consequence, we find that the bootstrap works. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 1006 1008 http://hdl.handle.net/10.1093/biomet/asn044 application/pdf Access to full text is restricted to subscribers. Jan Beyersmann Martin Schumacher

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:169-1862009-04-05RePEc:oup:biomet

article Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorized into marginal and conditional methods. The former integrate out analytically the infinite-dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the Gibbs sampler. Conditional methods impute the Dirichlet process and update it as a component of the Gibbs sampler. Since this requires imputation of an infinite-dimensional process, implementation of the conditional method has relied on finite approximations. In this paper, we show how to avoid such approximations by designing two novel Markov chain Monte Carlo algorithms which sample from the exact posterior distribution of quantities of interest. The approximations are avoided by the new technique of retrospective sampling. We also show how the algorithms can obtain samples from functionals of the Dirichlet process. The marginal and the conditional methods are compared and a careful simulation study is included, which involves a non-conjugate model, different datasets and prior specifications. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 169 186 http://hdl.handle.net/10.1093/biomet/asm086 application/pdf Access to full text is restricted to subscribers. Omiros Papaspiliopoulos Gareth O. Roberts

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:715-7272009-04-05RePEc:oup:biomet

article This paper considers the problem of comparing a new treatment with a control based on multiple endpoints. The hypotheses are formulated with the goal of showing that the treatment is equivalent, i.e. not inferior, on all endpoints and superior on at least one endpoint compared to the control, where thresholds for equivalence and superiority are specified for each endpoint. Roy's (1953) union-intersection and Berger's (1982) intersection-union principles are employed to derive the basic test. It is shown that the critical constants required for the union-intersection test of superiority can be sharpened by a careful analysis of its type I error rate. The composite UI-IU test is illustrated by an example and compared in a simulation study to alternative tests proposed by Bloch et al. (2001) and Perlman & Wu (2004). The Bloch et al. test does not control the type I error rate because of its nonmonotone nature, and is hence not recommended. The UI-IU and the Perlman & Wu tests both control the type I error rate, but the latter test generally has a slightly higher power. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 715 727 Ajit C. Tamhane

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:85-982009-04-05RePEc:oup:biomet

article We propose a nonparametric method for identifying parsimony and for producing a statistically efficient estimator of a large covariance matrix. We reparameterise a covariance matrix through the modified Cholesky decomposition of its inverse or the one-step-ahead predictive representation of the vector of responses and reduce the nonintuitive task of modelling covariance matrices to the familiar task of model selection and estimation for a sequence of regression models. The Cholesky factor containing these regression coefficients is likely to have many off-diagonal elements that are zero or close to zero. Penalised normal likelihoods in this situation with L-sub-1 and L-sub-2 penalities are shown to be closely related to Tibshirani's (1996) <EM t="s">LASSO approach and to ridge regression. Adding either penalty to the likelihood helps to produce more stable estimators by introducing shrinkage to the elements in the Cholesky factor, while, because of its singularity, the L-sub-1 penalty will set some elements to zero and produce interpretable models. An algorithm is developed for computing the estimator and selecting the tuning parameter. The proposed maximum penalised likelihood estimator is illustrated using simulation and a real dataset involving estimation of a 102 × 102 covariance matrix. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 85 98 http://hdl.handle.net/10.1093/biomet/93.1.85 text/html Access to full text is restricted to subscribers. Jianhua Z. Huang Naiping Liu Mohsen Pourahmadi Linxu Liu

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:613-6282009-04-05RePEc:oup:biomet

article Seasonally persistent models were first introduced by Andel (1986) and Gray et al. (1989) to extend autoregressive moving-average and fractionally differenced models and to encompass long-memory quasi-periodic behaviour. These models are, for certain ranges of parameters, stationary, and we prove here that the behaviour of the periodogram and other tapered estimators cannot be simply extended from the work of Kunsch (1986) and Hurvich & Beltrao (1993) on long memory induced by a pole at the origin. We demonstrate that potentially large both positive and negative bias can be found from the same value of the long-memory parameter, and that the new distribution can be easily written down in the case of Gaussian processes. We also consider using both the cosine taper and the sine taper. The extended least squares estimator is also considered in this context. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 613 628 Sofia C. Olhede

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:279-2942009-04-05RePEc:oup:biomet

article We consider different ways of constructing weighted Hochberg-type step-up multiple test procedures including closed procedures based on weighted Simes tests and their conservative step-up short-cuts, and step-up counterparts of two weighted Holm procedures. It is shown that the step-up counterparts have some serious pitfalls such as lack of familywise error rate control and lack of monotonicity in rejection decisions in terms of p-values. Therefore an exact closed procedure appears to be the best alternative, its only drawback being lack of simple stepwise structure. A conservative step-up short-cut to the closed procedure may be used instead, but with accompanying loss of power. Simulations are used to study the familywise error rate and power properties of the competing procedures for independent and correlated p-values. Although many of the results of this paper are negative, they are useful in highlighting the need for caution when procedures with similar pitfalls may be used. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 279 294 http://hdl.handle.net/10.1093/biomet/asn018 application/pdf Access to full text is restricted to subscribers. Ajit C. Tamhane Lingyun Liu

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:659-6682009-04-05RePEc:oup:biomet

article A unified estimation procedure is proposed for the analysis of censored data using linear transformation models, which include the proportional hazards model and the proportional odds model as special cases. This procedure is easily implemented numerically and its validity does not rely on the assumption of independence between the covariates and the censoring variable. The estimator is the same as the Cox partial likelihood estimator in the case of the proportional hazards model. Moreover, the asymptotic variance of the proposed estimator has a closed form and its variance estimator is easily obtained by plug-in rules. The method is illustrated by simulation and is applied to the Veterans' Administration lung cancer data. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 659 668 Kani Chen

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:37-472009-04-05RePEc:oup:biomet

article We consider the problem of using data in studies with an unobserved treatment/response variable in order to evaluate average causal effects, when cause-effect relationships between variables can be described by a directed acyclic graph and the corresponding recursive factorization of a joint distribution. The paper proposes graphical criteria to test whether average causal effects are identifiable even if a treatment/response variable is unobserved. If the answer is affirmative, we provide further formulations for average causal effects from the observed data. The graphical criteria enable us to evaluate average causal effects when it is difficult to observe a treatment/response variable. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 37 47 http://hdl.handle.net/10.1093/biomet/asm005 application/pdf Access to full text is restricted to subscribers. Manabu Kuroki

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:992-9982009-04-05RePEc:oup:biomet

article A random sample is drawn from a distribution which admits a minimal sufficient statistic for the parameters. The Gibbs sampler is proposed to generate samples, called conditionally sufficient or co-sufficient samples, from the conditional distribution of the sample given its value of the sufficient statistic. The procedure is illustrated for the gamma distribution. Co-sufficient samples may be used to give exact tests of fit; for the gamma distribution these are compared for size and power with approximate tests based on the parametric bootstrap. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 992 998 http://hdl.handle.net/10.1093/biomet/asm065 application/pdf Access to full text is restricted to subscribers. Richard A. Lockhart Federico J. O'Reilly Michael A. Stephens

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:409-4232009-04-05RePEc:oup:biomet

article We consider a nonlinear regression problem with predictors with measurement error. We assume that the response is related to unknown linear combinations of a p-dimensional predictor vector through an unknown link function. Instead of observing the predictors, we observe a surrogate vector with the property that its expectation is linearly related to the predictor vector with constant variance. We use an important linear transformation of the surrogates. Based on the transformed variables, we develop the modified Principal Hessian Directions method for estimating the subspace of the effective dimension-reduction space. We derive the asymptotic variances of the modified Principal Hessian Directions estimators. Several examples are reported and comparisons are made with the sliced inverse regression method of Carroll & Li (1992). Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 409 423 Heng-Hui Lue

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:513-5282009-04-05RePEc:oup:biomet

article A Bayesian approach is presented for spatially adaptive nonparametric regression where the regression function is modelled as a mixture of splines. Each component spline in the mixture has associated with it a smoothing parameter which is defined over a local region of the covariate space. These local regions overlap such that individual data points may lie simultaneously in multiple regions. Consequently each component spline has attached to it a weight at each point of the covariate space and, by allowing the weight of each component spline to vary across the covariate space, a spatially adaptive estimate of the regression function is obtained. The number of mixing components is chosen using a modification of the Bayesian information criteria. We study the procedure analytically and show by simulation that it compares favourably to three competing techniques. These techniques are the Bayesian regression splines estimator of Smith & Kohn (1996), the hybrid adaptive spline estimator of Luo & Wahba (1997) and the automatic Bayesian curve fitting estimator of Denison et al. (1998). The methodology is illustrated by modelling global air temperature anomalies. All the computations are carried out efficiently using Markov chain Monte Carlo. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 513 528 Sally A. Wood

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:167-1832009-04-05RePEc:oup:biomet

article We use the properties of independence estimating equations to adjust the 'independence' loglikelihood function in the presence of clustering. The proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix, which is easily calculated. The methodology competes favourably with established techniques based on independence estimating equations; we provide some insight as to why this is so. The adjustment is applied to examples relating to the modelling of wind speed in Europe and annual maximum temperatures in the U.K. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 167 183 http://hdl.handle.net/10.1093/biomet/asm015 application/pdf Access to full text is restricted to subscribers. Richard E. Chandler Steven Bate

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:601-6192009-04-05RePEc:oup:biomet

article We propose a modelling framework to study the relationship between two paired longitudinally observed variables. The data for each variable are viewed as smooth curves measured at discrete time-points plus random errors. While the curves for each variable are summarized using a few important principal components, the association of the two longitudinal variables is modelled through the association of the principal component scores. We use penalized splines to model the mean curves and the principal component curves, and cast the proposed model into a mixed-effects model framework for model fitting, prediction and inference. The proposed method can be applied in the difficult case in which the measurement times are irregular and sparse and may differ widely across individuals. Use of functional principal components enhances model interpretation and improves statistical and numerical stability of the parameter estimates. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 601 619 http://hdl.handle.net/10.1093/biomet/asn035 application/pdf Access to full text is restricted to subscribers. Lan Zhou Jianhua Z. Huang Raymond J. Carroll

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:763-7832009-04-05RePEc:oup:biomet

article We consider estimation of the received treatment effect on a dichotomous outcome in randomised trials with non-compliance. We explore inference about the parameters of the structural mean models of Robins (1994, 1997) and Robins et al. (1999). We show that, in contrast to the additive and multiplicative structural mean models for continuous and count outcomes, unbiased estimating functions for a nonzero (structural) treatment effect parameter do not exist in the presence of many continuous and discrete baseline covariates, even when the randomisation probabilities are known. The best that can be hoped for are estimators, such as those proposed in this paper, that are guaranteed both to estimate consistently the (null) treatment effect when the null hypothesis of no treatment effect is true and to have small bias when the true treatment effect is close to but not equal to zero. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 763 783 http://hdl.handle.net/10.1093/biomet/91.4.763 text/html Access to full text is restricted to subscribers. James Robins Andrea Rotnitzky

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:724-7302009-04-05RePEc:oup:biomet

article We propose a recursive algorithm as a more useful alternative to the Brook expansion for the joint distribution of a vector of random variables when the original formulation is in terms of the corresponding full conditional distributions, as occurs for Markov random fields. Usually, in practical applications, the computational load will still be excessive but then the algorithm can be used to obtain the componentwise full conditionals of a system after marginalising over some variables or the joint distribution of subsets of the variables, conditioned on values of the remainder, which is required for block Gibbs sampling. As an illustrative example, we apply the algorithm in the simplest nontrivial setting of hidden Markov chains. More important, we demonstrate how it applies to Markov random fields on regular lattices and to perfect block Gibbs sampling for binary systems. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 724 730 Francesco Bartolucci

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:399-4092009-04-05RePEc:oup:biomet

article A graphical model for multivariate time series is a concept extended by Dahlhaus (2000) from that for a random vector to a multivariate time series. We propose a test statistic for identifying the model based on the Kullback-Leibler divergence between two graphical models. The null distribution is shown to be asymptotically normal with mean and variance which depend just on the dimensions of the graphs. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 399 409 http://hdl.handle.net/10.1093/biomet/93.2.399 text/html Access to full text is restricted to subscribers. Yasumasa Matsuda

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:487-4952009-04-05RePEc:oup:biomet

article We present a goodness-of-fit test for the logistic regression model under case-control sampling. The test statistic is constructed via a discrepancy between two competing kernel density estimators of the underlying conditional distributions given case-control status. The proposed goodness-of-fit test is shown to compare very favourably with previously proposed tests for case-control sampling in terms of power. The test statistic can be easily computed as a quadratic form in the residuals from a prospective logistic regression maximum likelihood fit. In addition, the proposed test is affine invariant and has an alternative representation in terms of empirical characteristic functions. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 487 495 http://hdl.handle.net/10.1093/biomet/asm033 application/pdf Access to full text is restricted to subscribers. Howard D. Bondell

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:225-2292009-04-05RePEc:oup:biomet

article The current literature on fractional factorial plans in block designs centres around orthogonal blocking which may not, however, always be attainable because of practical restrictions on the block size. For general factorials, including asymmetric ones, sufficient conditions are indicated in this paper for a main effect plan to be universally optimal under possibly non-orthogonal blocking. A construction procedure is given using generalised Youden designs in conjunction with orthogonal arrays. We also illustrate how the procedure can be applied to obtain optimal main effect plans in the practically important situation where each factor has two or three levels and the block size is small. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 225 229 Rahul Mukerjee

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:243-2482009-04-05RePEc:oup:biomet

article We consider maximum likelihood estimation of the size of a target population to which has been added a known number of planted individuals. The standard equal-catchability model used in mark-recapture is assumed to be applicable to the augmented population. After proving the unimodality of the profile likelihood for the target population size, we obtain both the maximum likelihood estimator of this size and interval estimators based on its asymptotic distribution. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 243 248 http://hdl.handle.net/10.1093/biomet/asm012 application/pdf Access to full text is restricted to subscribers. I. B. J. Goudie P. E. Jupp J. Ashbridge

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:955-9732009-04-05RePEc:oup:biomet

article We introduce so-called analytic stationary wavelet transform thresholding where, using the discrete Hilbert transform, we create a complex-valued 'analytic' vector from which an amplitude vector is defined. Thresholding of a real-valued wavelet coefficient at some transform level is carried out according to the corresponding value in this amplitude vector; relevant statistical results follow from properties of the discrete Hilbert transform. Analytic stationary wavelet transform thresholding is found to produce consistently a reduced mean squared error compared to using standard stationary wavelet transform, or 'cycle spinning', thresholding. For signals with extensive oscillations at some transform levels, this improvement is very marked. Furthermore we show that our thresholding test is invariant to phase shifts in the data, whereas, if complex wavelet filters are being used, the filters must be analytic or anti-analytic at each level of the wavelet transform. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 955 973 http://hdl.handle.net/10.1093/biomet/91.4.955 text/html Access to full text is restricted to subscribers. Sofia C. Olhede Andrew T. Walden

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:465-4702009-04-05RePEc:oup:biomet

article Sufficient conditions are given for balanced incomplete block designs with block sizes three and four to be saturated minimal fractions of m items taken in mixture sizes of n &equals; 3 and 4 for estimating the contrasts of item means and two-item specific mixing effects. Such fractions are useful for investigations involving mixtures of crops, drugs, marketing practices and other systems using mixtures of items. The balanced incomplete block design with parameters &ngr; &equals; 6 and k &equals; 4 is shown to be a saturated minimal fraction for estimating contrasts of item means and two-item and three-item specific mixing effects. This is a continuation of the work of Federer & Raghavarao (1987) and Federer (2001). Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 465 470 Damaraju Raghavarao

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:95-1122009-04-05RePEc:oup:biomet

article We propose pseudo empirical best linear unbiased estimators of small-area means based on natural exponential family quadratic variance function models when the basic data consist of survey-weighted estimators of these means, area-specific covariates and certain summary measures involving the weights. We also provide explicit approximate mean squared errors of these estimators in the spirit of Prasad & Rao (1990), and these estimators can be readily evaluated. A simulation study is undertaken to evaluate the performance of the proposed inferential procedure. We estimate also the proportion of poor children in the 5--17 years age-group for the different counties in one of the states in the United States. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 95 112 Malay Ghosh

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:157-1692009-04-05RePEc:oup:biomet

article We propose a Poisson modelling approach to nested random effects Cox proportional hazards models. An important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects. The orthodox best linear unbiased predictor approach to random effects Poisson modelling techniques enables us to justify appropriate consistency and optimality. The explicit expressions for the random effects given by our approach facilitate incorporation of a relatively large number of random effects. The use of the proposed methods is illustrated through the reanalysis of data from a large-scale cohort study of particulate air pollution and mortality previously reported by Pope et al. (1995). Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 157 169 Renjun Ma

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:379-3922009-04-05RePEc:oup:biomet

article We consider a semiparametric generalisation of normal-theory discriminant analysis. The semiparametric model assumes that, after unspecified univariate monotone transformations, the class distributions are multivariate normal. We introduce an estimation procedure based on the distribution quantiles, in which the parameters of the semiparametric model are estimated directly without estimating the nonparametric transformations. The procedure is computationally fast and the estimation accuracy is shown to have the usual parametric rate. The relationship between the method and more general nonparametric discriminant analysis is discussed. The semiparametric specification of the class densities is a submodel of the nonparametric log density functional analysis of variance model in which the main effects are completely nonparametric but the interaction terms are specified semiparametrically. Simulations and real examples are used to illustrate the procedure. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 379 392 Y. Lin

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:919-9312009-04-05RePEc:oup:biomet

article Small area estimation methods typically combine direct estimates from a survey with predictions from a model in order to obtain estimates of population quantities with reduced mean squared error. When the auxiliary information used in the model is measured with error, using a small area estimator such as the Fay--Herriot estimator while ignoring measurement error may be worse than simply using the direct estimator. We propose a new small area estimator that accounts for sampling variability in the auxiliary information, and derive its properties, in particular showing that it is approximately unbiased. The estimator is applied to predict quantities measured in the U.S. National Health and Nutrition Examination Survey, with auxiliary information from the U.S. National Health Interview Survey. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 919 931 http://hdl.handle.net/10.1093/biomet/asn048 application/pdf Access to full text is restricted to subscribers. Lynn M. R. Ybarra Sharon L. Lohr

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:81-942009-04-05RePEc:oup:biomet

article Suppose that a consistent estimator for an infinite-dimensional parameter can be readily obtained via a set of estimating functions which has a 'good' local linear approximation around the true value of the parameter. However, it may be difficult to estimate the variance function of this estimator well. We show that, if the set of estimating functions evaluated at the true parameter value is 'asymptotically pivotal', then the 'fiducial' distribution of the parameter can be used to approximate the distribution of this consistent estimator. We present three examples to illustrate that the corresponding inference for the parameter can be made via a simple simulation technique without involving complex, high-dimensional nonparametric density estimates. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 81 94 M. A. Goldwasser

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:587-5992009-04-05RePEc:oup:biomet

article We consider a multivariate random effects model for clustered binary data that is useful when interest focuses on the association structure among clustered observations. Based on a vector of gamma random effects and a complementary log-log link function, the model yields a likelihood that has closed form, making a frequentist approach to model-fitting straightforward. This closed form yields several advantages over existing methods, including easy inspection of model identifiability and straightforward adjustment for nonrandom ascertainment of subjects, such as that which occurs in family studies of disease aggregation. We use the proposed model to analyse two different binary datasets concerning disease outcome data from a familial aggregation study of breast and ovarian cancer in women and loss of heterozygosity outcomes from a brain tumour study. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 587 599 http://hdl.handle.net/10.1093/biomet/93.3.587 text/html Access to full text is restricted to subscribers. Brent A. Coull E. Andres Houseman Rebecca A. Betensky

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:905-9192009-04-05RePEc:oup:biomet

article Most statistical solutions to the problem of statistical inference with missing data involve integration or expectation. This can be done in many ways: directly or indirectly, analytically or numerically, deterministically or stochastically. Missing-data problems can be formulated in terms of latent random variables, so that hierarchical likelihood methods of Lee & Nelder (1996) can be applied to missing-value problems to provide one solution to the problem of integration of the likelihood. The resulting methods effectively use a Laplace approximation to the marginal likelihood with an additional adjustment to the measures of precision to accommodate the estimation of the fixed effects parameters. We first consider missing at random cases where problems are simpler to handle because the integration does not need to involve the missing-value mechanism and then consider missing not at random cases. We also study tobit regression and refit the missing not at random selection model to the antidepressant trial data analyzed in Diggle & Kenward (1994). Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 905 919 http://hdl.handle.net/10.1093/biomet/asm063 application/pdf Access to full text is restricted to subscribers. Sung-Cheol Yun Youngjo Lee Michael G. Kenward

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:737-7462009-04-05RePEc:oup:biomet

article We investigate the mean squared error of the Stein--James estimator for the mean when the observations are generated from a Gaussian vector stationary process with dimension greater than two. First, assuming that the process is short-memory, we evaluate the mean squared error, and compare it with that for the sample mean. Then a sufficient condition for the Stein--James estimator to improve upon the sample mean is given in terms of the spectral density matrix around the origin. We repeat the analysis for Gaussian vector long-memory processes. Numerical examples clearly illuminate the Stein--James phenomenon for dependent samples. The results have the potential to improve the usual trend estimator in time series regression models. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 737 746 http://hdl.handle.net/10.1093/biomet/92.3.737 text/html Access to full text is restricted to subscribers. Masanobu Taniguchi Junichi Hirukawa

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:489-4902009-04-05RePEc:oup:biomet

article Engen & Lillegård (1997) presented a general method for doing Monte Carlo simulations conditioned on a sufficient statistic. The basic idea was to adjust the parameter values in the corresponding unconditional simulation so that the actual value of the sufficient statistic is obtained, and the claim was that if this adjustment is unique then the modified simulation is from the conditional distribution. Unfortunately the claim is not correct, as shown by a counterexample. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 489 490 Bo Henry Lindqvist

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:347-3582009-04-05RePEc:oup:biomet

article We consider a local least-squares criterion for aligning multiple time series fragments differing by locations and show the consistency of the time-lag estimator and the asymptotic normality of the location estimator. We apply the criterion to the problem of aligning 50 glacial varve fragments and construct a 3000-year surrogate for global temperature. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 347 358 http://hdl.handle.net/10.1093/biomet/asm023 application/pdf Access to full text is restricted to subscribers. K. Mukherjee R. H. Shumway K. L. Verosub

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:655-6682009-04-05RePEc:oup:biomet

article Methods are introduced for regressing points on the surface of one sphere on points on another. Complex variables and stereographic projection are used to deal with theoretical problems of directional statistics much as they have been used historically to deal with problems in non-Euclidean geometry. The complex plane harbours the group of Möbius transformations, and stereographic projection is used as a bridge to map these Möbius transforms to regression link functions on the surface of a unit sphere. A special form for these links is introduced which employs the complex plane and stereographic projection to effect angular scale changes on the sphere. The family of special forms is closed under orthogonal transformations of the dependent variable and Möbius transformations of the independent variable, and incorporates independence and proper and improper rotations as special cases. Parameter estimation and inference are exemplified using the von Mises--Fisher spherical distribution and vectorcardiogram data. All statistical results and calculations have been formulated in the real domain. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 655 668 T. D. Downs

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:769-7862009-04-05RePEc:oup:biomet

article We consider the problem of evaluating the probability of discovering a certain number of new species in a new sample of population units, conditional on the number of species recorded in a basic sample. We use a Bayesian nonparametric approach. The different species proportions are assumed to be random and the observations from the population exchangeable. We provide a Bayesian estimator, under quadratic loss, for the probability of discovering new species which can be compared with well-known frequentist estimators. The results we obtain are illustrated through a numerical example and an application to a genomic dataset concerning the discovery of new genes by sequencing additional single-read sequences of cdna fragments. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 769 786 http://hdl.handle.net/10.1093/biomet/asm061 application/pdf Access to full text is restricted to subscribers. Antonio Lijoi Ramsés H. Mena Igor Prünster

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:831-8462009-04-05RePEc:oup:biomet

article Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalised spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. They allow straightforward extensions to multiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically normal, and they admit consistent variance estimation using familiar design-based methods. Data-driven penalty selection is considered in the context of unequal probability sampling designs. Simulation experiments show that the estimators are more efficient than parametric regression estimators when the parametric model is incorrectly specified, while being approximately as efficient when the parametric specification is correct. An example using Forest Health Monitoring survey data from the U.S. Forest Service demonstrates the applicability of the methodology in the context of a two-phase survey with multiple auxiliary variables. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 831 846 http://hdl.handle.net/10.1093/biomet/92.4.831 text/html Access to full text is restricted to subscribers. F. J. Breidt G. Claeskens J. D. Opsomer

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:655-6692009-04-05RePEc:oup:biomet

article The product-limit estimator calculated from data subject to random left-truncation relies on the testable assumption of quasi-independence between the failure time and the truncation time. In this paper, we propose a model for a truncated sample of pairs (X-sub-i,Y-sub-i) satisfying Y-sub-i > X-sub-i. A possible dependency between the truncation time and the variable of interest is modelled with a parametric family of copulas. The model also features a distribution function F-sub-X(.) and a survival distribution S-sub-Y(.) associated with the marginal behaviours of X and Y in the observable region Y > X. Semiparametric estimators for these two functions are proposed; they do not make any parametric assumption about either F-sub-X(.) or S-sub-Y(.). We derive an estimator for the copula parameter α based on the conditional Kendall's tau. We generalise the copula-graphic estimators of Zheng & Klein (1995) to truncated variables. The asymptotic distributions of all these estimators are then investigated. The methods are illustrated with a real dataset on HIV infection by transfusion and by simulations. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 655 669 http://hdl.handle.net/10.1093/biomet/93.3.655 text/html Access to full text is restricted to subscribers. Lajmi Lakhal Chaieb Louis-Paul Rivest Belkacem Abdous

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:165-1762009-04-05RePEc:oup:biomet

article Classical regression analysis is usually performed in two steps. In a first step an appropriate model is identified to describe the data-generating process and in a second step statistical inference is performed in the identified model. In this paper we investigate a sequential and a non-sequential design strategy, which take into account these different goals of the analysis for a class of nested models. It is demonstrated that non-sequential designs usually identify the 'correct' model with a higher probability than sequential methods. Although non-sequential designs can never be guaranteed to achieve the best possible efficiency in the 'correct' model, it is demonstrated by means of a simulation study that for realistic sample sizes the efficiencies of the non-sequential designs for the estimation of the parameters in the 'correct' model are at least as high as the corresponding efficiencies of the sequential methods. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 165 176 Holger Dette

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:159-1822009-04-05RePEc:oup:biomet

article A new model for the simultaneous eigenstructure of multiple covariance matrices is proposed. The model is much more flexible than existing models and subsumes most of them as special cases. A Fisher scoring algorithm for computing maximum likelihood estimates of the parameters under normality is given. Asymptotic distributions of the estimators are derived under normality as well as under arbitrary distributions having finite fourth-order cumulants. Special attention is given to elliptically contoured distributions. Likelihood ratio tests are described and sufficient conditions are given under which the test statistics are asymptotically distributed as chi-squared random variables. Procedures are derived for evaluating Bartlett corrections under normality. Some conjectures made by Flury (1988) are verified; others are refuted. A small simulation study of the adequacy of the Bartlett correction is described and the new procedures are illustrated on two datasets. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 159 182 Robert J. Boik

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:351-3632009-04-05RePEc:oup:biomet

article The R package spatstat provides a very flexible and useful framework for analysing spatial point patterns. A fundamental feature is a procedure for fitting spatial point process models depending on covariates. However, in practice one often faces incomplete observation of the covariates and this leads to parameter estimation error which is difficult to quantify. In this paper, we introduce a Monte Carlo version of the estimating function used in spatstat for fitting inhomogeneous Poisson processes and certain inhomogeneous cluster processes. For this modified estimating function, it is feasible to obtain the asymptotic distribution of the parameter estimators in the case of incomplete covariate information. This allows a study of the loss of efficiency due to the missing covariate data. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 351 363 http://hdl.handle.net/10.1093/biomet/asn020 application/pdf Access to full text is restricted to subscribers. Rasmus Waagepetersen

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:403-1142009-04-05RePEc:oup:biomet

article We present a nonparametric estimator of genotype-specific age-at-onset distributions from kin-cohort data. Standard error calculations are derived and the methodology is illustrated through an analysis of the influence of mutations of the Parkin gene on Parkinson's disease. Semiparametric efficiency considerations are briefly discussed. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 403 114 http://hdl.handle.net/10.1093/biomet/asm027 application/pdf Access to full text is restricted to subscribers. Yuanjia Wang Lorraine N. Clark Karen Marder Daniel Rabinowitz

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:459-4682009-04-05RePEc:oup:biomet

article We consider nested row-column designs where each of the row and column component designs is specified. For the case that each of the component designs has second-order balance, we define such a nested row-column design to be special if it is generally balanced, with the smallest possible number of canonical treatment contrasts having the lower canonical efficiency factor in both components. We show that if any special row-column design exists then it is A-optimal over all nested row-column designs with the given components. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 459 468 http://hdl.handle.net/10.1093/biomet/asm039 application/pdf Access to full text is restricted to subscribers. R. A. Bailey E. R. Williams

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:779-7982009-04-05RePEc:oup:biomet

article We propose an alternative to Kendall's shape space for reflection shapes of configurations in <inline-formula><inline-graphic xlink:href="asn050ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach embeds the space of such shapes into the space <inline-formula><inline-graphic xlink:href="asn050ilm2.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> of (k - 1) × (k - 1) real symmetric positive semidefinite matrices, which is the closure of an open subset of a Euclidean space, and defines mean shape as the natural projection of Euclidean means in <inline-formula><inline-graphic xlink:href="asn050ilm3.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> on to the embedded copy of the shape space. This approach has strong connections with multi-dimensional scaling, and the mean shape so defined gives good approximations to other commonly used definitions of mean shape. We also use standard perturbation arguments for eigenvalues and eigenvectors to obtain a central limit theorem which then enables the application of standard statistical techniques to shape analysis in two or more dimensions. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 779 798 http://hdl.handle.net/10.1093/biomet/asn050 application/pdf Access to full text is restricted to subscribers. Ian L. Dryden Alfred Kume Huiling Le Andrew T. A. Wood

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:443-4582009-04-05RePEc:oup:biomet

article The problem of evaluating the goodness of the predictive distributions of hierarchical Bayesian and empirical Bayes models is investigated. A Bayesian predictive information criterion is proposed as an estimator of the posterior mean of the expected loglikelihood of the predictive distribution when the specified family of probability distributions does not contain the true distribution. The proposed criterion is developed by correcting the asymptotic bias of the posterior mean of the loglikelihood as an estimator of its expected loglikelihood. In the evaluation of hierarchical Bayesian models with random effects, regardless of our parametric focus, the proposed criterion considers the bias correction of the posterior mean of the marginal loglikelihood because it requires a consistent parameter estimator. The use of the bootstrap in model evaluation is also discussed. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 443 458 http://hdl.handle.net/10.1093/biomet/asm017 application/pdf Access to full text is restricted to subscribers. Tomohiro Ando

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:957-9642009-04-05RePEc:oup:biomet

article Suppose that, under a two-level hierarchical model, the distribution of the vector of random parameters is known or can be estimated well. The data are generated via a fixed, but unobservable, realisation of the vector. We derive the smallest confidence region for a specific component of this random vector under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is especially appealing when one deals with data generated under a highly parallel structure. The new proposal is illustrated with a dataset from a multi-centre clinical study and also with one from a typical microarray experiment. The performance of our procedure is examined via simulation studies. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 957 964 http://hdl.handle.net/10.1093/biomet/92.4.957 text/html Access to full text is restricted to subscribers. Hajime Uno Lu Tian L. J. Wei

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:703-7152009-04-05RePEc:oup:biomet

article In many applications, researchers are interested in estimating the mean of a multivariate normal random vector whose components are subject to order restrictions. Various authors have demonstrated that the likelihood-based methodology may perform poorly under certain conditions for such problems. The problem is much harder when the underlying covariance matrix is nondiagonal. In this paper a simple iterative algorithm is introduced that can be used for estimating the mean of a multivariate normal population when the components are subject to any order restriction. The proposed methodology is illustrated through an application to human reproductive hormone data. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 703 715 http://hdl.handle.net/10.1093/biomet/92.3.703 text/html Access to full text is restricted to subscribers. Shyamal D. Peddada David B. Dunson Xiaofeng Tan

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:573-5852009-04-05RePEc:oup:biomet

article We introduce new robust small area estimation procedures based on area-level models. We first find influence functions corresponding to each individual area-level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation. Next, based on these influence functions, properly standardized, we propose some new robust Bayes and empirical Bayes small area estimators. The mean squared errors and estimated mean squared errors of these estimators are also found. A small simulation study compares the performance of the robust and the regular empirical Bayes estimators. When the model variance is larger than the sample variance, the proposed robust empirical Bayes estimators are superior. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 573 585 http://hdl.handle.net/10.1093/biomet/asn030 application/pdf Access to full text is restricted to subscribers. Malay Ghosh Tapabrata Maiti Ananya Roy

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:667-6782009-04-05RePEc:oup:biomet

article We consider mixture models in which the components of data vectors from any given subpopulation are statistically independent, or independent in blocks. We argue that if, under this condition of independence, we take a nonparametric view of the problem and allow the number of subpopulations to be quite general, the distributions and mixing proportions can often be estimated root-n consistently. Indeed, we show that, if the data are k-variate and there are p subpopulations, then for each p &ges; 2 there is a minimal value of k, k-sub-p say, such that the mixture problem is always nonparametrically identifiable, and all distributions and mixture proportions are nonparametrically identifiable when k &ges; k-sub-p. We treat the case p &equals; 2 in detail, and there we show how to construct explicit distribution, density and mixture-proportion estimators, converging at conventional rates. Other values of p can be addressed using a similar approach, although the methodology becomes rapidly more complex as p increases. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 667 678 http://hdl.handle.net/10.1093/biomet/92.3.667 text/html Access to full text is restricted to subscribers. Peter Hall Amnon Neeman Reza Pakyari Ryan Elmore

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:462-4692009-04-05RePEc:oup:biomet

article It is shown that both the simple form of the Rasch model for binary data and a generalisation are essentially equivalent to special dichotomised Gaussian models. In these the underlying Gaussian structure is of single factor form; that is, the correlations between the binary variables arise via a single underlying variable, called in psychometrics a latent trait. The implications for scoring of the binary variables are discussed, in particular regarding the scoring system as in effect estimating the latent trait. In particular, the role of the simple sum score, in effect the total number of 'successes', is examined. Relations with the principal component analysis of binary data are outlined and some connections with the quadratic exponential binary model are sketched. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 462 469 D. R. Cox

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:947-9602009-04-05RePEc:oup:biomet

article We consider a class of semiparametric normal transformation models for right-censored bivariate failure times. Nonparametric hazard rate models are transformed to a standard normal model and a joint normal distribution is assumed for the bivariate vector of transformed variates. A semiparametric maximum likelihood estimation procedure is developed for estimating the marginal survival distribution and the pairwise correlation parameters. This produces an efficient estimator of the correlation parameter of the semiparametric normal transformation model, which characterizes the dependence of bivariate survival outcomes. In addition, a simple positive-mass-redistribution algorithm can be used to implement the estimation procedures. Since the likelihood function involves infinite-dimensional parameters, empirical process theory is utilized to study the asymptotic properties of the proposed estimators, which are shown to be consistent, asymptotically normal and semiparametric efficient. A simple estimator for the variance of the estimates is derived. Finite sample performance is evaluated via extensive simulations. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 947 960 http://hdl.handle.net/10.1093/biomet/asn049 application/pdf Access to full text is restricted to subscribers. Yi Li Ross L. Prentice Xihong Lin

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:633-6462009-04-05RePEc:oup:biomet

article A Bayesian adaptive design is proposed for a comparative two-armed clinical trial using decision-theoretic approaches. A loss function is specified, based on the cost for each patient and the costs of making incorrect decisions at the end of a trial. At each interim analysis, the decision to terminate or to continue the trial is based on the expected loss function while concurrently incorporating efficacy, futility and cost. The maximum number of interim analyses is determined adaptively by the observed data. We derive explicit connections between the loss function and the frequentist error rates, so that the desired frequentist properties can be maintained for regulatory settings. The operating characteristics of the design can be evaluated on frequentist grounds. Extensive simulations are carried out to compare the proposed design with existing ones. The design is general enough to accommodate both continuous and discrete types of data. We illustrate the methods with an animal study evaluating a medical treatment for cardiac arrest. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 633 646 http://hdl.handle.net/10.1093/biomet/92.3.633 text/html Access to full text is restricted to subscribers. Yi Cheng Yu Shen

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:213-2272009-04-05RePEc:oup:biomet

article Multivariate extreme value distributions arise as the limiting distributions of normalised componentwise maxima. They are often used to model multivariate data that can be regarded as the componentwise maxima of some unobserved underlying multivariate process. In many applications we have extra information. We often know the locations of the maxima within the underlying process. If the process is temporal this knowledge is frequently available through the dates on which the maxima are recorded. We show how to incorporate this extra information into maximum likelihood procedures. Asymptotic and small-sample efficiency results are presented for the dependence parameter in the logistic parametric sub-class of bivariate extreme value distributions. We conclude with an application to sea levels. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 213 227 http://hdl.handle.net/10.1093/biomet/92.1.213 text/html Access to full text is restricted to subscribers. Alec Stephenson Jonathan Tawn

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:738-7422009-04-05RePEc:oup:biomet

article The one-factor model restricts the covariance structure of the observed variables on the basis of assumptions about their relationship with an unobserved variable. It is hard to justify these assumptions on substantive or empirical grounds. In this paper, alternative measurement models are proposed that are based on exchangeability of variables after admissible scale transformations. They provide an alternative interpretation of the model and do not involve unobserved variables. They also yield a new one-factor model for sum scales. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 738 742 Henk Kelderman

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:399-4182009-04-05RePEc:oup:biomet

article We consider the problem of maximum-likelihood estimation in case-control studies of gene-environment associations with disease when genetic and environmental exposures can be assumed to be independent in the underlying population. Traditional logistic regression analysis may not be efficient in this setting. We study the semiparametric maximum likelihood estimates of logistic regression parameters that exploit the gene-environment independence assumption and leave the distribution of the environmental exposures to be nonparametric. We use a profile-likelihood technique to derive a simple algorithm for obtaining the estimator and we study the asymptotic theory. The results are extended to situations where genetic and environmental factors are independent conditional on some other factors. Simulation studies investigate small-sample properties. The method is illustrated using data from a case-control study designed to investigate the interplay of BRCA1&sol;2 mutations and oral contraceptive use in the aetiology of ovarian cancer. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 399 418 http://hdl.handle.net/10.1093/biomet/92.2.399 text/html Access to full text is restricted to subscribers. Nilanjan Chatterjee Raymond J. Carroll

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:985-9912009-04-05RePEc:oup:biomet

article Monte Carlo importance sampling for evaluating numerical integration is discussed. We consider a parametric family of sampling distributions and propose the use of the sampling distribution estimated by maximum likelihood. The proposed method of importance sampling using the estimated sampling distribution is shown to improve the asymptotic variance of the ordinary method using the true sampling distribution. The argument is closely related to the discussion of the paradox in Henmi & Eguchi (2004). We focus on a condition under which the estimated integration value obtained by the proposed method has asymptotic zero variance. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 985 991 http://hdl.handle.net/10.1093/biomet/asm076 application/pdf Access to full text is restricted to subscribers. Masayuki Henmi Ryo Yoshida Shinto Eguchi

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:987-9912009-04-05RePEc:oup:biomet

article We consider forecasting from age-period-cohort models, as well as from the extended chain-ladder model. The parameters of these models are known only to be identified up to linear trends. Forecasts from such models may therefore depend on arbitrary linear trends. A condition for invariant forecasts is proposed. A number of standard forecast models are analysed. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 987 991 http://hdl.handle.net/10.1093/biomet/asn038 application/pdf Access to full text is restricted to subscribers. D. Kuang B. Nielsen J. P. Nielsen

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:976-9812009-04-05RePEc:oup:biomet

article In many applications, particularly in genetics, samples are drawn under complex ascertainment rules. For example, families may only be selected for study if two or more siblings have trait values exceeding some threshold. The correct likelihood for inference in such situations involves the probabilities of ascertainment, and these are frequently intractable. A consistent, but not fully efficient, method of analysis of such studies is proposed. The main idea is to augment the data with additional pseudo-observations simulated under the ascertainment scheme, and to analyse using a conditional likelihood for discrimination between true observations and pseudo-observations. Ascertainment probabilities cancel in this likelihood. The method is illustrated with a simple example involving left-truncated failure times. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 976 981 David Clayton

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:387-4022009-04-05RePEc:oup:biomet

article To assess treatment efficacy in clinical trials, certain clinical outcomes are repeatedly measured over time for the same subject. The difference in their means may characterize a treatment effect. Since treatment effectiveness lag and saturation times may exist, erosion of treatment effect often occurs during the observation period. Instead of using models based on ad hoc parametric or purely nonparametric time-varying coefficients, we model the treatment effectiveness durations, which are the time intervals between the lag and saturation times. Then we use some mean response models to include such treatment effectiveness durations. Our methodology is demonstrated by simulations and analysis of a landmark <sc>HIV</sc>/<sc>AIDS</sc> clinical trial of short-course nevirapine against mother-to-child <sc>HIV</sc> vertical transmission during labour and delivery. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 387 402 http://hdl.handle.net/10.1093/biomet/asm019 application/pdf Access to full text is restricted to subscribers. Y. Q. Chen J. Yang S. Cheng J. B. Jackson

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:153-1642009-04-05RePEc:oup:biomet

article Outside the field of statistics, the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal, such as multiple operationalism or a dose-response relationship. These useful suggestions are typically informal and qualitative. A quantitative measure, design sensitivity, is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases. Several common strategies are then evaluated in terms of their contribution to design sensitivity. A related method for computing the power of a sensitivity analysis is also developed. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 153 164 Paul R. Rosenbaum

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:315-3282009-04-05RePEc:oup:biomet

article The problem of testing for the equality of k distribution functions under Case 2 interval censoring is studied and a supremum-type test statistic is proposed based on the differences between the nonparametric maximum likelihood estimator and the so-called leveraged bootstrap estimator of the k underlying distributions. The proposed test is distributionfree and consistent against all alternatives. As the main results hold for a wide range of resampling sizes, a data-driven method is suggested for determining the size of each leveraged bootstrap sample. Another advantage of the test is that it can detect different distributions with equal means or heavy crossover. Simulation studies indicate that the test performs quite well with a moderate sample size. Finally, a slightly modified version of the test is applied to breast cosmesis data. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 315 328 http://hdl.handle.net/10.1093/biomet/93.2.315 text/html Access to full text is restricted to subscribers. Kam-Chuen Yuen Jian Shi Lixing Zhu

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:251-2702009-04-05RePEc:oup:biomet

article Marginal likelihood and conditional likelihood are often used for eliminating nuisance parameters. For a parametric model, it is well known that the full likelihood can be decomposed into the product of a conditional likelihood and a marginal likelihood. This property is less transparent in a nonparametric or semiparametric likelihood setting. In this paper we show that this nice parametric likelihood property can be carried over to the empirical likelihood world. We discuss applications in case-control studies, genetical linkage analysis, genetical quantitative traits analysis, tuberculosis infection data and unordered-paired data, all of which can be treated as semiparametric finite mixture models. We consider the estimation problem in detail in the simplest case of unordered-paired data where we can only observe the minimum and maximum values of two random variables; the identities of the minimum and maximum values are lost. The profile empirical likelihood approach is used for maximum semiparametric likelihood estimation. We present some large-sample results along with a simulation study. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 251 270 http://hdl.handle.net/10.1093/biomet/92.2.251 text/html Access to full text is restricted to subscribers. Jing Qin Biao Zhang

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:603-6122009-04-05RePEc:oup:biomet

article Higher-order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on &thgr;. A modified likelihood ratio statistic is proposed that follows its asymptotic distribution to a high degree of approximation, and this statistic is illustrated on several examples. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 603 612 Thomas A. Severini

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:159-1712009-04-05RePEc:oup:biomet

article We derive nonparametric procedures for testing for and against likelihood ratio ordering in the two-population setting with continuous distributions. We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions F and G. In particular, we focus on testing equality of F and G versus likelihood ratio ordering and testing for a violation of likelihood ratio ordering. For both testing problems, we propose area-based and sup-norm-based test statistics, derive appropriate limiting distributions, and provide simulation results that characterise the performance of our procedures. We illustrate our methods using data from a controlled experiment involving the effects of radiation on mice. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 159 171 http://hdl.handle.net/10.1093/biomet/92.1.159 text/html Access to full text is restricted to subscribers. Christopher A. Carolan Joshua M. Tebbs

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:199-2082009-04-05RePEc:oup:biomet

article Panel count data arise when a recurrent event is under investigation and each study subject is observed only at discrete time points. In this situation, observed data include only the numbers of occurrences of the event of interest between observation time points and no information is available on subjects between their observation time points. We propose a nonparametric test for comparing the point processes characterising the recurrent event when only panel count data are available. The asymptotic distribution of the test statistic is derived and a simulation study is conducted to evaluate its performance. The method is illustrated using data from a medical follow-up study. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 199 208 Jianguo Sun

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:502-5082009-04-05RePEc:oup:biomet

article When performing multi-component significance tests with multiply-imputed datasets, analysts can use a Wald-like test statistic and a reference F-distribution. The currently employed degrees of freedom in the denominator of this F-distribution are derived assuming an infinite sample size. For modest complete-data sample sizes, this degrees of freedom can be unrealistic; for example, it may exceed the complete-data degrees of freedom. This paper presents an alternative denominator degrees of freedom that is always less than or equal to the complete-data denominator degrees of freedom, and equals the currently employed denominator degrees of freedom for infinite sample sizes. Its advantages over the currently employed degrees of freedom are illustrated with a simulation. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 502 508 http://hdl.handle.net/10.1093/biomet/asm028 application/pdf Access to full text is restricted to subscribers. Jerome P. Reiter

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:827-8392009-04-05RePEc:oup:biomet

article We develop a proposal or importance density for state space models with a nonlinear non-Gaussian observation vector y ∼ p(y¦θ) and an unobserved linear Gaussian signal vector θ ∼ p(θ). The proposal density is obtained from the Laplace approximation of the smoothing density p(θ¦y). We present efficient algorithms to calculate the mode of p(θ¦y) and to sample from the proposal density. The samples can be used for importance sampling and Markov chain Monte Carlo methods. The new results allow the application of these methods to state space models where the observation density p(y¦θ) is not log-concave. Additional results are presented that lead to computationally efficient implementations. We illustrate the methods for the stochastic volatility model with leverage. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 827 839 http://hdl.handle.net/10.1093/biomet/asm074 application/pdf Access to full text is restricted to subscribers. Borus Jungbacker Siem Jan Koopman

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:411-4212009-04-05RePEc:oup:biomet

article We consider tests of the null hypothesis that g covariance matrices have a partial common principal component subspace of dimension s. Our approach uses a dimensionality matrix which has its rank equal to s when the hypothesis holds. The test can then be based on a statistic computed from the eigenvalues of an estimate of this dimensionality matrix. The asymptotic distribution of this statistic is that of a linear combination of independent one-degree-of-freedom chi-squared random variables. Simulation results indicate that this test yields significance levels that come closer to the nominal level than do those of a previously proposed method. The procedure is also extended to a test that g correlation matrices have a partial common principal component subspace. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 411 421 James R. Schott

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:937-9502009-04-05RePEc:oup:biomet

article A traditional approach to statistical inference is to identify the true or best model first with little or no consideration of the specific goal of inference in the model identification stage. Can the pursuit of the true model also lead to optimal regression estimation? In model selection, it is well known that BIC is consistent in selecting the true model, and AIC is minimax-rate optimal for estimating the regression function. A recent promising direction is adaptive model selection, in which, in contrast to AIC and BIC, the penalty term is data-dependent. Some theoretical and empirical results have been obtained in support of adaptive model selection, but it is still not clear if it can really share the strengths of AIC and BIC. Model combining or averaging has attracted increasing attention as a means to overcome the model selection uncertainty. Can Bayesian model averaging be optimal for estimating the regression function in a minimax sense? We show that the answers to these questions are basically in the negative: for any model selection criterion to be consistent, it must behave suboptimally for estimating the regression function in terms of minimax rate of covergence; and Bayesian model averaging cannot be minimax-rate optimal for regression estimation. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 937 950 http://hdl.handle.net/10.1093/biomet/92.4.937 text/html Access to full text is restricted to subscribers. Yuhong Yang

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:732-7402009-04-05RePEc:oup:biomet

article A rank-based regression method is proposed for repeated measurements data. It is a generalisation of the classical Wilcoxon--Mann--Whitney rank statistic for independent observations. The method is valid under a weak condition on the error terms that can accommodate certain heteroscedasticity and within-subject dependency. The asymptotic normality of the proposed estimator is proved using empirical process theory. A variance estimator, shown to be consistent, is also constructed. The proposed method is illustrated using data from a clinical trial on treating labour pain. Robustness and efficiency of the estimator is demonstrated in simulation studies. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 732 740 Sin-Ho Jung

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:982-9842009-04-05RePEc:oup:biomet

article The relationship between marginal and conditional distributions of binary random variables is analysed via a log-linear model. Conditions for the Yule--Simpson effect are established and the implications for latent class analysis examined. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 982 984 D. R. Cox

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:751-7572009-04-05RePEc:oup:biomet

article Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r&plus;1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(S-super-r&plus;1) computations, as opposed to O(S-super-n) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 751 757 R. Reeves

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:1006-10132009-04-05RePEc:oup:biomet

article Chen & Dunson ([3]) have proposed a modified Cholesky decomposition of the form σ &equals; D L L′D for a covariance matrix where D is a diagonal matrix with entries proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix solely determining its correlation matrix. This total separation of variance and correlation is definitely a major advantage over the more traditional modified Cholesky decomposition of the form LD-super-2L′, (Pourahmadi, [13]). We show that, though the variance and correlation parameters of the former decomposition are separate, they are not asymptotically orthogonal and that the estimation of the new parameters could be more demanding computationally. We also provide statistical interpretation for the entries of L and D as certain moving average parameters and innovation variances and indicate how the existing likelihood procedures can be employed to estimate the new parameters. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 1006 1013 http://hdl.handle.net/10.1093/biomet/asm073 application/pdf Access to full text is restricted to subscribers. Mohsen Pourahmadi

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:641-6542009-04-05RePEc:oup:biomet

article A new ordering scheme for defining quantiles of the multivariate distribution of a stopping time and a stopped stochastic process is introduced. This ordering scheme is used in conjunction with resampling methods to construct confidence intervals for a population mean following a group sequential test with random group sizes, and for the regression parameter of a proportional hazards model following a time-sequential clinical trial with censored survival data. It is shown that this approach resolves the long-standing difficulties in inference due to two different time scales in time-sequential trials, and that the confidence intervals thus constructed have coverage probabilities close to the nominal values and provide marked improvements over those based on alternative ordering schemes and normal approximations. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 641 654 http://hdl.handle.net/10.1093/biomet/93.3.641 text/html Access to full text is restricted to subscribers. Tze Leung Lai Wenzhi Li

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:939-9522009-04-05RePEc:oup:biomet

article A modification to the pairwise likelihood method is proposed, which aims to improve the estimation of the marginal distribution parameters. This is achieved by replacing the pairwise likelihood score equations, for estimating such parameters, by the optimal linear combinations of the marginal score functions. A further advantage of the proposed estimator of marginal parameters, over pairwise likelihood, is that it is robust to misspecification of the bivariate distributions as long as the univariate marginal distributions are correctly specified. While alternating logistic regression can be seen as a special case of the proposed method, it is shown that an existing generalization of alternating logistic regression applicable to ordinal data is not the same as and is inferior to the proposed method because it replaces certain conditional densities by pseudodensities that assume working independence. The fitting of the multivariate negative binomial distribution is another scenario involving intractable likelihood that calls for the use of pairwise likelihood methods, and the superiority of the modified method is demonstrated in a simulation study. Two examples, based on the analyses of salamander mating and patient-controlled analgesia data, demonstrate the usefulness of the proposed method. The possibility of combining optimally the pairwise, rather than marginal, scores is also considered and its difficulty and potential are discussed. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 939 952 http://hdl.handle.net/10.1093/biomet/asm051 application/pdf Access to full text is restricted to subscribers. Anthony Y. C. Kuk

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:185-1982009-04-05RePEc:oup:biomet

article We consider partially linear models of the form Y = X-super-Tβ + ν(Z) + ɛ when the response variable Y is sometimes missing with missingness probability π depending on (X, Z), and the covariate X is measured with error, where ν(z) is an unspecified smooth function. The missingness structure is therefore missing not at random, rather than the usual missing at random. We propose a class of semiparametric estimators for the parameter of interest β, as well as for the population mean E(Y). The resulting estimators are shown to be consistent and asymptotically normal under general assumptions. To construct a confidence region for β, we also propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. The proposed methods are applied to an AIDS clinical trial dataset. A simulation study is also reported. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 185 198 http://hdl.handle.net/10.1093/biomet/asm010 application/pdf Access to full text is restricted to subscribers. Hua Liang Suojin Wang Raymond J. Carroll

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:529-5412009-04-05RePEc:oup:biomet

article In this paper, we show that the distribution function of survival times is identified, up to a one-parameter family of distribution functions, based on information from case-control current status data. With supplementary information on the population frequency of cases relative to controls, a simple weighted version of the nonparametric maximum likelihood estimator for prospective current status data provides a natural estimator for case-control samples. Following the parametric results of Scott & Wild (1997), we show that this estimator is, in fact, the nonparametric maximum likelihood estimator. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 529 541 Nicholas P. Jewell

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:735-7412009-04-05RePEc:oup:biomet

article We provide a simple estimation procedure for a general frailty model for the analysis of prospective correlated failure times. The large-sample properties of the proposed estimators of both the regression coefficient vector and the dependence parameter are described, and consistent variance estimators are given. A brief outline of the proofs is given. In a simulation study under the widely used gamma frailty model, our proposed approach was found to have essentially the same efficiency as the EM-based maximum likelihood approach considered by other authors, with negligible difference between the standard errors of the two estimators. However, the proposed approach provides a framework capable of handling general frailty distributions with finite moments and yields an explicit consistent variance estimator. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 735 741 http://hdl.handle.net/10.1093/biomet/93.3.735 text/html Access to full text is restricted to subscribers. Malka Gorfine David M. Zucker Li Hsu

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:269-2872009-04-05RePEc:oup:biomet

article The fully nonparametric model for nonlinear analysis of covariance, proposed in Akritas et al. (2000), is considered in the context of censored observations. Under this model, the distributions for each factor level combination and covariate value are not restricted to comply to any parametric or semiparametric model. The data can be continuous or ordinal categorical. The possibility of different shapes of covariate effect in different factor level combinations is also allowed. This generality is useful whenever modelling assumptions such as additive risks, proportional hazards or proportional odds appear suspect. Test statistics are obtained for the nonparametric hypotheses of no main effect and of no interaction effect which adjusts for the presence of a covariate. They are quadratic forms based on averages over the covariate values of Beran estimators of the conditional distribution of the survival time given each covariate value. The derivation of the asymptotic &khgr;-super-2 distribution of the test statistics uses a recently-obtained asymptotic representation of the Beran estimator as average of independent random variables. A real-data set is analysed and results of simulation studies are reported. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 269 287 Yunling Du

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:743-7502009-04-05RePEc:oup:biomet

article We study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug-in rule for bandwidth choice, optimising the coverage accuracy of interval estimators. The performance of this approach is explored. Our preferred technique is based on asymptotic approximation, rather than a more sophisticated approach using the bootstrap, since the latter requires a multiplicity of smoothing parameters all of which must be chosen in nonstandard ways. It is shown that the asymptotic method can give very good performance. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 743 750 Peter Hall

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:250-2502009-04-05RePEc:oup:biomet

article 1 2005 92 March Biometrika 250 250 http://hdl.handle.net/10.1093/biomet/92.1.250 text/html Access to full text is restricted to subscribers. Jing Qin Biao Zhang

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:627-6402009-04-05RePEc:oup:biomet

article A class of semiparametric transformation models is proposed to characterise the effects of possibly time-varying covariates on the intensity functions of counting processes. The class includes the proportional intensity model and linear transformation models as special cases. Nonparametric maximum likelihood estimators are developed for the regression parameters and cumulative intensity functions of these models based on censored data. The estimators are shown to be consistent and asymptotically normal. The limiting variances for the estimators of the regression parameters achieve the semi-parametric efficient bounds and can be consistently estimated. The limiting variances for the estimators of smooth functionals of the cumulative intensity function can also be consistently estimated. Simulation studies reveal that the proposed inference procedures perform well in practical settings. Two medical studies are provided. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 627 640 http://hdl.handle.net/10.1093/biomet/93.3.627 text/html Access to full text is restricted to subscribers. Donglin Zeng D. Y. Lin

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:992-9962009-04-05RePEc:oup:biomet

article It is common, in particular in observational studies in epidemiology, to impose stratification to adjust for possible effects of age and other variables on the binary outcome of interest. Overstratification may lower the precision of the estimated effects of interest. Understratification risks bias. These issues are studied analytically. Asymptotic results show that loss of efficiency depends on the true effect and on a measure of the average imbalance across strata between exposed and unexposed individuals. Bias depends on the correlation between stratum-specific size imbalances and event rates in the unexposed. Approximate results are also given. An example is used. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 992 996 http://hdl.handle.net/10.1093/biomet/asn039 application/pdf Access to full text is restricted to subscribers. B. L. De Stavola D. R. Cox

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:99-1122009-04-05RePEc:oup:biomet

article The minimum Hellinger distance estimator is known to have desirable properties in terms of robustness and efficiency. We propose an approximate minimum Hellinger distance estimator by adapting the approach to grouped data from a continuous distribution. It is easier to compute the approximate version for either the continuous data or the grouped data. Given certain conditions on the model distribution and reasonable grouping rules, the approximate minimum Hellinger distance estimator is shown to be consistent and asymptotically normal. Furthermore, it is robust and can be asymptotically as efficient as the maximum likelihood estimator. The merit of the estimator is demonstrated through simulation studies and real data examples. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 99 112 http://hdl.handle.net/10.1093/biomet/93.1.99 text/html Access to full text is restricted to subscribers. Nan Lin Xuming He

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:813-8292009-04-05RePEc:oup:biomet

article There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 813 829 http://hdl.handle.net/10.1093/biomet/asn053 application/pdf Access to full text is restricted to subscribers. Bo Li Marc G. Genton Michael Sherman

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:497-5052009-04-05RePEc:oup:biomet

article We use saddlepoint approximation to derive credible intervals for Bayesian wavelet regression estimates. Simulations show that the resulting intervals perform better than the best existing method. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 497 505 C. Semadeni

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:893-9042009-04-05RePEc:oup:biomet

article We propose a robust curve and surface estimator based on M-type estimators and penalty-based smoothing. This approach also includes an application to wavelet regression. The concept of pseudo data, a transformation of the robust additive model to the one with bounded errors, is used to derive some theoretical properties and also motivate a computational algorithm. The resulting algorithm, termed the es-algorithm, is computationally fast and provides a simple way of choosing the amount of smoothing. Moreover, it is easily described, straightforwardly implemented and can be extended to other wavelet regression settings such as irregularly spaced data and image denoising. Results from a simulation study and real data examples demonstrate the promising empirical properties of the proposed approach. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 893 904 http://hdl.handle.net/10.1093/biomet/asm064 application/pdf Access to full text is restricted to subscribers. Hee-Seok Oh Douglas W. Nychka Thomas C. M. Lee

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:119-1332009-04-05RePEc:oup:biomet

article We present a method for extracting information about both the scale and trend of local components of an inhomogeneous function in a nonparametric generalised linear model. Our multiscale framework combines recursive partitions, which allow for the incorporation of scale in a natural manner, with systems of piecewise polynomials supported on the partition intervals, which serve to summarise the smooth trend within each interval. Our estimators are formulated as solutions of complexity-penalised likelihood optimisations, where the penalty seeks to limit the number of intervals used to model the data. The actual calculation of the estimators may be accomplished using standard software routines for generalised linear models, within the context of efficient, tree-based, polynomial-time algorithms. A risk analysis shows that these estimators achieve the same asymptotic rates in the nonparametric generalised linear model as the classical wavelet-based estimators in the Gaussian 'function plus noise' model, for suitably defined ranges of Besov spaces. Numerical simulations show that the method tends to perform at least as well as, and often better than, alternative wavelet-based methodologies in the context of finite samples, while applications to gamma-ray burst data in astronomy and packet loss data in computer network tra.c analysis confirm its practical relevance. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 119 133 http://hdl.handle.net/10.1093/biomet/92.1.119 text/html Access to full text is restricted to subscribers. Eric D. Kolaczyk Robert D. Nowak

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:937-9512009-04-05RePEc:oup:biomet

article We show that the model-calibration estimator for the finite population mean, which was proposed by Wu & Sitter (2001) through an intuitive argument, is optimal among a class of calibration estimators. We also present optimal calibration estimators for the finite population distribution function, the population variance, the variance of a linear estimator and other quadratic finite population functions under a unified framework. The proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified. A limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial. The question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology. Some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 937 951 Changbao Wu

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:729-7372009-04-05RePEc:oup:biomet

article For likelihood-based inference involving distributions in which high-dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single qx1 vector of observations is observed are examined. Conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied. Some examples are analysed in detail. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 729 737 D. R. Cox

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:163-1732009-04-05RePEc:oup:biomet

article We develop a generalized Bayesian information criterion for regression model selection. The new criterion relaxes the usually strong distributional assumption associated with Schwarz's BIC by adopting a Wilcoxon-type dispersion function and appropriately adjusting the penalty term. We establish that the Wilcoxon-type generalized BIC preserves the consistency of Schwarz's BIC without the need to assume a parametric likelihood. We also show that it outperforms Schwarz's BIC with heavier-tailed data in the sense that asymptotically it can yield substantially smaller L-sub-2 risk. On the other hand, when the data are normally distributed, both criteria have similar L-sub-2 risk. The new criterion function is convex and can be conveniently computed using existing statistical software. Our proposal provides a flexible yet highly efficient alternative to Schwarz's BIC; at the same time, it broadens the scope of Wilcoxon inference, which has played a fundamental role in classical nonparametric analysis. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 163 173 http://hdl.handle.net/10.1093/biomet/asn060 application/pdf Access to full text is restricted to subscribers. Lan Wang

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:799-8122009-04-05RePEc:oup:biomet

article We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations. They possess useful equivariance properties and provide a clear alternative to spectral models for covariance matrices. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 799 812 http://hdl.handle.net/10.1093/biomet/asn052 application/pdf Access to full text is restricted to subscribers. R. Dennis Cook Liliana Forzani

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:267-2832009-04-05RePEc:oup:biomet

article We consider the multivariate location problem with cluster-correlated data. A family of multivariate weighted sign tests is introduced for which observations from different clusters can receive different weights. Under weak assumptions, the test statistic is asymptotically distributed as a chi-squared random variable as the number of clusters goes to infinity. The asymptotic distribution of the test statistic is also given for a local alternative model under multivariate normality. Optimal weights maximizing Pitman asymptotic efficiency are provided. These weights depend on the cluster sizes and on the intracluster correlation. Several approaches for estimating these weights are presented. Using Pitman asymptotic efficiency, we show that appropriate weighting can increase substantially the efficiency compared to a test that gives the same weight to each cluster. A multivariate weighted t-test is also introduced. The finite-sample performance of the weighted sign test is explored through a simulation study which shows that the proposed approach is very competitive. A real data example illustrates the practical application of the methodology. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 267 283 http://hdl.handle.net/10.1093/biomet/asm026 application/pdf Access to full text is restricted to subscribers. Denis Larocque Jaakko Nevalainen Hannu Oja

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:873-8922009-04-05RePEc:oup:biomet

article Very often in survival analysis one has to study martingale integrals where the integrand is not predictable and where the counting process theory of martingales is not directly applicable, as for example in nonparametric and semiparametric applications where the integrand is based on a pilot estimate. We call this the predictability issue in survival analysis. The problem has been resolved by approximations of the integrand by predictable functions which have been justified by ad hoc procedures. We present a general approach to the solution of this problem. The usefulness of the approach is shown in three applications. In particular, we argue that earlier ad hoc procedures do not work in higher-dimensional smoothing problems in survival analysis. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 873 892 http://hdl.handle.net/10.1093/biomet/asm062 application/pdf Access to full text is restricted to subscribers. Enno Mammen Jens Perch Nielsen

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:861-8722009-04-05RePEc:oup:biomet

article We study a test comparing the full Aalen additive hazards model and the change-point model, and suggest how to estimate the parameters of the change-point model. We also study a test for no change-point effect. Both tests are provided with large sample properties and a resampling method is applied to obtain p-values. The finite-sample properties of the proposed inference procedures and estimators are assessed through a simulation study. The methods are further applied to a dataset concerning myocardial infarction. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 861 872 http://hdl.handle.net/10.1093/biomet/asm054 application/pdf Access to full text is restricted to subscribers. Torben Martinussen Thomas H. Scheike

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:229-2332009-04-05RePEc:oup:biomet

article Part of the folklore of capture-recapture experiments is that ignoring heterogeneity of capture probabilities results in a downward bias. This has been based on experience and simulation studies but is often interpreted as being due to individuals with lower capture probabilities. Here estimating equation arguments are used to show that the effect on Horvitz--Thompson-type estimators of ignoring heterogeneity in capture-recapture experiments is to introduce a downward bias. The arguments are extended to continuous-time experiments and to an influence function constructed to determine the effect of a small number of individuals with heterogeneous capture probabilities in an otherwise homogeneous population and the influence function is shown to be negative. The downward bias holds even if the small number of heterogeneous individuals have capture probabilities larger than the homogeneous majority, and this is confirmed by simulations. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 229 233 http://hdl.handle.net/10.1093/biomet/92.1.229 text/html Access to full text is restricted to subscribers. Wen-Han Hwang Richard Huggins

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:724-7312009-04-05RePEc:oup:biomet

article It is well known that the maximum likelihood fit of the logistic regression parameters can be greatly affected by atypical observations. Several robust alternatives have been proposed. However, if we consider the model from the case-control viewpoint, it is clear that current techniques can exhibit poor behaviour in many common situations. A new robust class of estimation procedures is introduced. The estimators are constructed via a minimum distance approach after identifying the model with a semiparametric biased sampling model. The approach is developed under the case-control sampling scheme, yet is shown to be applicable under prospective sampling as well. A weighted Cramer--von Mises distance is used as an illustrative example of the methodology. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 724 731 http://hdl.handle.net/10.1093/biomet/92.3.724 text/html Access to full text is restricted to subscribers. Howard D. Bondell

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:899-9122009-04-05RePEc:oup:biomet

article The proportional hazards model makes two major assumptions: the hazard ratio is constant over time, and the relationship between the hazard and continuous covariates is log-linear. Methods exist for checking and relaxing each of these assumptions, but in both cases the methods rely on the other assumption being true. Problems can occur if neither of the assumptions is appropriate, or even if only one of the assumptions is appropriate but it is not known which. We propose a new kind of residual for checking the two assumptions simultaneously. The smoothed residuals provide a flexible estimate of the hazard ratio, which may deviate from the standard proportional hazards model by having a time-dependent hazard ratio, transformed covariates or both. The methods are illustrated using data from the Medical Research Council's myeloma trials. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 899 912 Peter D. Sasieni

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:87-992009-04-05RePEc:oup:biomet

article In a large class of hazard models with proportional unobserved heterogeneity, the distribution of the heterogeneity among survivors converges to a gamma distribution. This convergence is often rapid. We derive this result as a general result for exponential mixtures and explore its implications for the specification and empirical analysis of univariate and multivariate duration models. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 87 99 http://hdl.handle.net/10.1093/biomet/asm013 application/pdf Access to full text is restricted to subscribers. Jaap H. Abbring Gerard J. Van Den Berg

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:891-9052009-04-05RePEc:oup:biomet

article In the generalized method of moments approach to longitudinal data analysis, unbiased estimating functions can be constructed to incorporate both the marginal mean and the correlation structure of the data. Increasing the number of parameters in the correlation structure corresponds to increasing the number of estimating functions. Thus, building a correlation model is equivalent to selecting estimating functions. This paper proposes a chi-squared test to choose informative unbiased estimating functions. We show that this methodology is useful for identifying which source of correlation it is important to incorporate when there are multiple possible sources of correlation. This method can also be applied to determine the optimal working correlation for the generalized estimating equation approach. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 891 905 http://hdl.handle.net/10.1093/biomet/asn051 application/pdf Access to full text is restricted to subscribers. Annie Qu J. Jack Lee Bruce G. Lindsay

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:758-7612009-04-05RePEc:oup:biomet

article A practically important but not so obvious result is that alternating logistic regression is invariant to permutations of the response variables within clusters. In this note, we give a short proof of the invariance result using a pairwise likelihood argument. The same proof can be used to establish invariance for a more general class of estimating equations based on conditional residuals. As it stands, the invariance theory is incomplete because existing standard error estimates are not invariant to permutations. To solve this problem we present a symmetrised version of the estimating equation and use it to obtain permutation-invariant standard errors. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 758 761 Anthony Y. C. Kuk

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:543-5572009-04-05RePEc:oup:biomet

article We propose a novel approach to estimating the mean difference between two highly skewed distributions. The method, which we call smooth quantile ratio estimation, smooths, over percentiles, the ratio of the quantiles of the two distributions. The method defines a large class of estimators, including the sample mean difference, the maximum likelihood estimator under log-normal samples and the L-estimator. We derive asymptotic properties such as consistency and asymptotic normality, and also provide a closed-form expression for the asymptotic variance. In a simulation study, we show that smooth quantile ratio estimation has lower mean squared error than several competitors, including the sample mean difference and the log-normal parametric estimator in several realistic situations. We apply the method to the 1987 National Medicare Expenditure Survey to estimate the difference in medical expenditures between persons suffering from the smoking attributable diseases, lung cancer and chronic obstructive pulmonary disease, and persons without these diseases. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 543 557 http://hdl.handle.net/10.1093/biomet/92.3.543 text/html Access to full text is restricted to subscribers. Francesca Dominici Leslie Cope Daniel Q. Naiman Scott L. Zeger

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:543-5512009-04-05RePEc:oup:biomet

article Test statistics from the weighted log-rank class are commonly used to compare treatment with control when there is right censoring. This paper uses saddlepoint methods to determine mid-p-values from the null permutation distributions of tests from the weighted log-rank class. Analytical saddlepoint computations replace the permutation simulations and provide mid-p-values that are virtually exact for all practical purposes. The speed of these saddlepoint computations makes it practicable to invert the weighted log-rank tests to determine nominal 95% confidence intervals for the treatment effect with right-censored data. Such analytical inversions lead to permutation confidence intervals that are easily computed and virtually identical to the exact intervals that would normally require massive amounts of simulation. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 543 551 http://hdl.handle.net/10.1093/biomet/asm060 application/pdf Access to full text is restricted to subscribers. Ehab F. Abd-Elfattah Ronald W. Butler

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:371-3852009-04-05RePEc:oup:biomet

article Frailty and copula models specify a parametric dependence structure for multivariate failure-time data. Estimation of some joint quantities can be highly sensitive to the assumed parametric form, and hence model fit is an important issue. This paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models. The approach is based on the cumulative sum of residuals that are calculated in bivariate time. The residuals reflect the difference between the observed and expected bivariate association structures. The proposed model-checking process is interpretable with a limiting distribution which can be approximated using the bootstrap. Simulations and a data example illustrate the practical application of the method. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 371 385 http://hdl.handle.net/10.1093/biomet/asm024 application/pdf Access to full text is restricted to subscribers. David V. Glidden

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:985-9902009-04-05RePEc:oup:biomet

article We consider the property of consistency and its relevance for determining the performance of the bootstrap. We analyse various parametric bootstrap approximations to the distributions of the Hodges and Stein estimators, whose behaviour is typical of that of super-efficient estimators employed in wavelet regression, kernel density estimation and nonparametric curve fitting. Our results reveal not only some of the difficulties in selecting good modifications to the intuitive bootstrap, but also that inconsistent bootstrap approximations may perform better than consistent versions even in large samples. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 985 990 Richard Samworth

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:1-172009-04-05RePEc:oup:biomet

article We model pairwise dependence of temporal maxima, such as annual maxima of precipitation, that have been recorded in space, either on a regular grid or at irregularly spaced locations. The construction of our estimators stems from the variogram concept. The asymptotic properties of our pairwise dependence estimators are established through properties of empirical processes. The performance of our approach is illustrated by simulations and by the treatment of a real dataset. In addition to bringing new results about the asymptotic behaviour of copula estimators, the latter being linked to first-order variograms, one main advantage of our approach is to propose a simple connection between extreme value theory and geostatistics. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 1 17 http://hdl.handle.net/10.1093/biomet/asp001 application/pdf Access to full text is restricted to subscribers. Philippe Naveau Armelle Guillou Daniel Cooley Jean Diebolt

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:567-5782009-04-05RePEc:oup:biomet

article Examples of clustered data include data from longitudinal studies and data sampled within groups. This paper proposes a regression analysis method for clustered data that optimally weights and combines contrasts of the data through a combination of estimating equations. Examples of combining between-cluster, within-cluster and longitudinal data contrasts are presented. The method results in increased estimation efficiency relative to generalised estimating equations with standard working correlation structures. The proposed method also simplifies modelling decisions regarding the true correlation structure of the data and avoids correlation parameter estimation. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 567 578 Julie A. Stoner

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:351-3702009-04-05RePEc:oup:biomet

article This paper focuses on the Akaike information criterion, AIC, for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and questions regarding the particular clusters in the data. We show that the AIC in current use is not appropriate for the focus on clusters, and we propose instead the conditional Akaike information and its corresponding criterion, the conditional AIC, cAIC. The penalty term in cAIC is related to the effective degrees of freedom ρ for a linear mixed model proposed by Hodges & Sargent (2001); ρ reflects an intermediate level of complexity between a fixed-effects model with no cluster effect and a corresponding model with fixed cluster effects. The cAIC is defined for both maximum likelihood and residual maximum likelihood estimation. A pharmacokinetics data application is used to illuminate the distinction between the two inference settings, and to illustrate the use of the conditional AIC in model selection. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 351 370 http://hdl.handle.net/10.1093/biomet/92.2.351 text/html Access to full text is restricted to subscribers. Florin Vaida Suzette Blanchard

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:491-5152009-04-05RePEc:oup:biomet

article There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934). Spirtes (1994), Spirtes et al. (1993) and Pearl & Verma (1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and&sol;or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are 'pointwise consistent', but 'uniformly consistent' tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as BIC or AIC. The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 491 515 James M. Robins

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:289-3022009-04-05RePEc:oup:biomet

article There is a well-known Bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors. The limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form, which we call partially informative normal. We derive necessary and sufficient conditions for the propriety of the posterior for this class of partially informative normal priors with noninformative priors on the variance components, a condition crucial for successful implementation of the Gibbs sampler. The results apply for fully Bayesian smoothing splines, thin-plate splines and L-splines, as well as models using intrinsic autoregressive priors. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 289 302 Paul L. Speckman

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:875-8892009-04-05RePEc:oup:biomet

article Data collected by scientists are increasingly in the form of trajectories or curves. Often these can be viewed as realizations of a composite process driven by both amplitude and time variation. We consider the situation in which functional variation is dominated by time variation, and develop a curve-synchronization method that uses every trajectory in the sample as a reference to obtain pairwise warping functions in the first step. These initial pairwise warping functions are then used to create improved estimators of the underlying individual warping functions in the second step. A truncated averaging process is used to obtain robust estimation of individual warping functions. The method compares well with other available time-synchronization approaches and is illustrated with Berkeley growth data and gene expression data for multiple sclerosis. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 875 889 http://hdl.handle.net/10.1093/biomet/asn047 application/pdf Access to full text is restricted to subscribers. Rong Tang Hans-Georg Müller

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:996-10022009-04-05RePEc:oup:biomet

article This paper is concerned with identification of a competing risks model with unknown transformations of latent failure times. The model includes, as special cases, competing risks versions of proportional hazards, mixed proportional hazards and accelerated failure time models. It is shown that covariate effects on latent failure times, cause-specific link functions and the joint survivor function of the disturbance terms can be identified without relying on modelling the dependence between latent failure times parametrically nor using an exclusion restriction among covariates. As a result, the paper provides an identification result about the joint survivor function of the latent failure times conditional on covariates. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 996 1002 http://hdl.handle.net/10.1093/biomet/93.4.996 text/html Access to full text is restricted to subscribers. Sokbae Lee

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:223-2322009-04-05RePEc:oup:biomet

article An unbiased test for the appropriateness of the simple linear regression model is presented. The null hypothesis is that the underlying regression function is indeed a line, and the alternative is that it is convex. The exact distribution for a likelihood ratio test statistic is that of a mixture of beta random variables, with the mixing distribution calculated from relative volumes of polyhedral convex cones determined by the convex shape restriction. Simulations show that the power of the test is favourable compared with the usual F-test against a quadratic model, for some nonquadratic choices of the underlying regression function. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 223 232 Mary C. Meyer

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:411-4242009-04-05RePEc:oup:biomet

article Properties of the periodogram are seldom studied in the setting of nonparametric regression, although that is the context in which the periodogram is widely applied in astronomy. There it is a competitor with more recent least-squares methods. The periodogram has the advantage of providing significant graphical insight into statistical and numerical aspects of the problem. However, as we show in the present paper, it also has drawbacks. The estimator that it produces has somewhat higher variance than its least-squares counterpart, and a periodogram-based approach is more prone to suffer difficulties caused by periodicity of the observation schedule. While the periodogram remains a very attractive tool, the information provided in this paper allows users to assess more readily the extent to which it can be relied upon in a nonparametric setting. This aspect of our contributions is discussed theoretically and illustrated by numerical studies involving a real dataset. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 411 424 http://hdl.handle.net/10.1093/biomet/93.2.411 text/html Access to full text is restricted to subscribers. Peter Hall Ming Li

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:345-3582009-04-05RePEc:oup:biomet

article Linear errors-in-covariables models are considered, assuming the availability of independent validation data on the covariables in addition to primary data on the response variable and surrogate covariables. We first develop an estimated empirical loglikelihood with the help of validation data and prove that its asymptotic distribution is that of a weighted sum of independent standard x-super-2-sub-1 random variables with unknown weights. By estimating the unknown weights consistently, we construct an estimated empirical likelihood confidence region for the regression parameter vector. We also suggest an adjusted empirical loglikelihood and prove that its asymptotic distribution is a standard x-super-2. To avoid estimating the unknown weights or the adjustment factor, we propose a partially smoothed bootstrap empirical loglikelihood for constructing a confidence region which has asymptotically correct coverage probability. A simulation study is conducted to compare the proposed methods with a method based on a normal approximation in terms of coverage accuracy and average length of the confidence interval. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 345 358 Qihua Wang

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:101-1182009-04-05RePEc:oup:biomet

article We introduce the generalized threshold mixed model for piecewise-linear stochastic regression with possibly nonnormal time-series data. It is assumed that the conditional probability distribution of the response variable belongs to the exponential family, and the conditional mean response is linked to some piecewise-linear stochastic regression function. We study the particular case where the response variable equals zero in the lower regime. Some large-sample properties of a likelihood-based estimation scheme are derived. Our approach is motivated by the need for modelling nonlinearity in serially correlated epizootic events. Data coming from monitoring conducted in a natural plague focus in Kazakhstan are used to illustrate this model by obtaining biologically meaningful conclusions regarding the threshold relationship between prevalence of plague and some covariates including past abundance of great gerbils and other climatic variables. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 101 118 http://hdl.handle.net/10.1093/biomet/asm006 application/pdf Access to full text is restricted to subscribers. Noelle I. Samia Kung-Sik Chan Nils Chr. Stenseth

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:1-172009-04-05RePEc:oup:biomet

article Standard approaches to semiparametric modelling of two-sample survival data are not appropriate when the two survival curves cross. We introduce a two-sample model that accommodates crossing survival curves. The two scalar parameters of the model have the interpretations of being the short-term and long-term hazard ratios respectively. The time-varying hazard ratio is expressed semiparametrically by the two scalar parameters and an unspecified baseline distribution. The new model includes the Cox model and the proportional odds model as submodels. For inference we use a pseudo maximum likelihood approach that can be expressed via some simple estimating equations, analogous to that for the maximum partial likelihood estimator of the Cox model, that provide consistent and asymptotically normal estimators. Simulation studies show that the estimators perform well for moderate sample sizes. We also illustrate the methods with a real-data example. The new model can be extended easily to the regression setting. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 1 17 http://hdl.handle.net/10.1093/biomet/92.1.1 text/html Access to full text is restricted to subscribers. Song Yang Ross Prentice

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:1025-10262009-04-05RePEc:oup:biomet

article Arising from an omitted term in a calculation in the Appendix, variance formulae in the paper should be adjusted. In particular, the constants in the numerators of equations (2·4) and (2·15) should be 6 rather than 18. Variances are, however, still higher than in the case of least-squares estimators. The changes are implied by the following corrections to the Appendix. On p. 423, 2cδΔ′-sub-cos(ω-super-(k)) should be included within braces on lines 11 and 17, and 2cδΔ′-sub-sin(ω-super-(k)) should be added within braces on lines 12 and 18, leading to the extra term 2cm-super- - 3/2{Δ′-sub-sin(ω-super-(k))Gamma-sub-sin-super-(k) &plus; Δ′-sub-cos(ω-super-(k))Gamma-sub-cos-super-(k)} on line 21. We are grateful to Barry Quinn for drawing our attention to this error. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 1025 1026 http://hdl.handle.net/10.1093/biomet/93.4.1025-b text/html Access to full text is restricted to subscribers. Peter Hall Ming Li

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:139-1562009-04-05RePEc:oup:biomet

article We present properties of a dependence measure that arises in the study of extreme values in multivariate and spatial problems. For multivariate problems the dependence measure characterises dependence at the bivariate level, for all pairs and all higher orders up to and including the dimension of the variable. Necessary and sufficient conditions are given for subsets of dependence measures to be self-consistent, that is to guarantee the existence of a distribution with such a subset of values for the dependence measure. For pairwise dependence, these conditions are given in terms of positive semidefinite matrices and non-differentiable, positive definite functions. We construct new nonparametric estimators for the dependence measure which, unlike all naive nonparametric estimators, impose these self-consistency properties. As the new estimators provide an improvement on the naive methods, both in terms of the inferential and interpretability properties, their use in exploratory extreme value analyses should aid the identification of appropriate dependence models. The methods are illustrated through an analysis of simulated multivariate data, which shows that a lack of self-consistency is frequently a problem with the existing estimators, and by a spatial analysis of daily rainfall extremes in south-west England, which finds a smooth decay in extremal dependence with distance. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 139 156 Martin Schlather

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:245-2502009-04-05RePEc:oup:biomet

article We have implemented a Lagrange multiplier test for the alternative hypothesis of a nonlinear continuous-time autoregressive model with the instantaneous mean having multiple degrees of nonlinearity. This test is an extension of a Lagrange multiplier test proposed by Tsai & Chan (2000), with the alternative model analogous to the model used in Tsay's (1986) discrete-time work. The performance of the test in the finite-sample case is compared with several existing tests for nonlinearity including Keenan's (1985) test, Petruccelli & Davies' (1986) test, Tsay's (1986, 1989) tests and Tsai & Chan's (2000) test. The comparison is based on simulated data from some linear autoregressive models, self-exciting threshold autoregressive models, bilinear models and the nonlinear continuous-time autoregressive models for which the Lagrange multiplier test is designed. In general, the test is more powerful than all the other tests. The test is further illustrated with the annual sunspot data and the lynx data. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 245 250 Henghsiu Tsai

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:975-9862009-04-05RePEc:oup:biomet

article A general family of distributions for the empirical modelling of ordered multivariate data is proposed. The family is based on, but greatly extends, the joint distribution of order statistics from an independent and identically distributed univariate sample. General properties, including marginal and conditional distributions, bivariate dependence, limiting distributions and links to the Dirichlet distribution are described. Univariate and bivariate special cases of the multivariate distributions, the latter including an equivalent rotated version, are considered. Two particular tractable special cases are stressed. The models are successfully and usefully fitted, by maximum likelihood, to meteorological data. The models are also applicable to data in which one variable is unconstrained and the other are all nonnegative. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 975 986 http://hdl.handle.net/10.1093/biomet/91.4.975 text/html Access to full text is restricted to subscribers. M. C. Jones P. V. Larsen

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:573-5862009-04-05RePEc:oup:biomet

article There are two treatments, each of which may be applied or withheld, yielding a 2 x 2 factorial arrangement with three degrees of freedom between groups. The differential effect of the two treatments is the effect of applying one treatment in lieu of the other. In randomised experiments, the differential effect is of no more or less interest than other treatment contrasts. Differential effects play a special role in certain observational studies in which treatments are not assigned to subjects at random, where differing outcomes may reflect biased assignments rather than effects caused by the treatments. Differential effects are immune to certain types of unobserved bias, called generic biases, which are associated with both treatments in a similar way. This is explored using several examples and models. Differential effects are not immune to differential biases, whose possible consequences are examined by sensitivity analysis. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 573 586 http://hdl.handle.net/10.1093/biomet/93.3.573 text/html Access to full text is restricted to subscribers. Paul R. Rosenbaum

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:613-6252009-04-05RePEc:oup:biomet

article There are a number of different models for crossover designs which take account of carryover effects. Since it seems plausible that a treatment with a large direct effect should generally have a larger carryover effect, Kempton et al. (2001) considered a model where the carryover effects are proportional to the direct effects. The advantage of this model lies in the fact that there are fewer parameters to be estimated. Its problem lies in the nonlinearity of the estimators. Kempton et al. (2001) considered the least squares estimator. They point out that this estimator is asymptotically equivalent to the estimator in a linear model which assumes the true parameters to be known. For this estimator they determine optimal designs numerically for some cases. The present paper generalises some of their results. Our results are derived with the help of a generalisation of the methods used in Kunert & Martin (2000). Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 613 625 http://hdl.handle.net/10.1093/biomet/93.3.613 text/html Access to full text is restricted to subscribers. R. A. Bailey J. Kunert

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:359-3692009-04-05RePEc:oup:biomet

article We consider the additive hazard model when some of the true covariates are measured only on a randomly selected validation set whereas auxiliary covariates are observed for all study subjects. An updated pseudoscore estimation approach is proposed for the parameters of the additive hazard model. It allows one to fit the model with auxiliary covariates, while leaving the baseline hazard unspecified. Asymptotic properties of the proposed estimators are established, and consistent standard error estimators are developed. Simulations demonstrate that the asymptotic approximations of the proposed estimates are adequate for practical use. A real example is used to illustrate the performance of the proposed method. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 359 369 http://hdl.handle.net/10.1093/biomet/asm016 application/pdf Access to full text is restricted to subscribers. Jiancheng Jiang Zhou Haibo

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:484-4892009-04-11RePEc:oup:biomet

article The results of Davies (1977, 1987) are extended to a linear model situation with unknown residual variance. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 484 489 Robert B. Davies

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:451-4582009-04-11RePEc:oup:biomet

article Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis-Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 451 458 http://hdl.handle.net/10.1093/biomet/93.2.451 text/html Access to full text is restricted to subscribers. J. Møller A. N. Pettitt R. Reeves K. K. Berthelsen

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:183-1962009-04-11RePEc:oup:biomet

article Conventionally, modelling of multivariate extremes has been based on the class of multivariate extreme value distributions. More recently, other classes have been developed, allowing for the possibility that, whilst dependence is observed at finite levels, the limit distribution is independent. A number of articles have shown this development to be important for accurate estimation of the extremal properties, both of theoretical processes and observed datasets. It has also been shown that, so far as dependence is concerned, the choice between modelling with either asymptotically dependent or asymptotically independent distributions can be far more influential than model choice within either of these two classes. In this paper we explore the issue of modelling across both classes, examining in particular the effect of uncertainty caused by lack of knowledge about the status of asymptotic dependence. This is achieved by new multivariate models whose parameter spaces are such that asymptotic dependence occurs on a boundary. Standard techniques in Bayesian inference, implemented through Markov chain Monte Carlo, enable inferences to be drawn that assign posterior probability mass to the boundary region. The techniques are illustrated on a set of oceanographic data for which previous analyses have shown that it is difficult to resolve the question of asymptotic dependence status, which is however important in model extrapolation. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 183 196 Stuart Coles

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:337-3502009-04-11RePEc:oup:biomet

article We study criteria for identifiability of path analysis models with one hidden variable. We first derive sufficient criteria for identification of models in which marginalisation is carried out over the hidden variable. The sufficient criteria are based on the structure of the directed acyclic graph associated with the path analysis model and can be derived from the graph. We treat further the identification of models when the hidden variable is conditioned on and establish connections with the extended skew-normal distribution. Finally it is shown that the derived conditions extend the existing graphical criteria for identification. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 337 350 http://hdl.handle.net/10.1093/biomet/92.2.337 text/html Access to full text is restricted to subscribers. Elena Stanghellini Nanny Wermuth

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:627-6462009-04-15RePEc:oup:biomet

article We study Ornstein-Uhlenbeck stochastic processes driven by Lévy processes, and extend them to more general non-Ornstein-Uhlenbeck models. In particular, we investigate the means of making the correlation structure in the volatility process more flexible. For one model, we implement a method for introducing quasi long-memory into the volatility model. We demonstrate that the models can be fitted to real share price returns data. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 627 646 http://hdl.handle.net/10.1093/biomet/asm048 application/pdf Access to full text is restricted to subscribers. Matthew P. S. Gander David A. Stephens

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:423-4362009-04-15RePEc:oup:biomet

article The present paper examines proportional goodness of fit to variables recorded on individuals, the variances and covariances of the variables, and the form and distances between individuals. No single plot displays all three optimally in the sense of least squares. However, even aspects which are non-optimally fitted by biplots and Benzecri plots often closely preserve the optimal fit. This is shown by means of a preservation-of-fit function which depends on the type of display and on the ratio of the second to the first singular value of the data matrix. This function is never below 0·5, so at least half the fit is always preserved, and it is close to 1 unless the ratio of the singular values is small. That explains the frequently observed similarity of the various biplots and the Benzecri plot and the fact that they usually lead to the same conclusions. It follows that in many applications it is reasonable to use either the symmetric biplot or the Benzecri plot or a compromise maximin preservation plot, and that the difference between these three is usually unimportant. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 423 436 K. Ruben Gabriel

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:243-2472009-04-15RePEc:oup:biomet

article We propose a method for constructing orthogonal or nearly orthogonal Latin hypercubes. The method yields a large Latin hypercube by coupling an orthogonal array of index unity with a small Latin hypercube. It is shown that the large Latin hypercube inherits the exact or near orthogonality of the small Latin hypercube. Thus, effort for searching for large Latin hypercubes, that are exactly or nearly orthogonal, can be focussed on finding small Latin hypercubes with the same property. We obtain a useful collection of orthogonal or nearly orthogonal Latin hypercubes, which have a large factor-to-run ratio and the results are often much more economical than existing methods. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 243 247 http://hdl.handle.net/10.1093/biomet/asn064 application/pdf Access to full text is restricted to subscribers. C. Devon Lin Rahul Mukerjee Boxin Tang

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:705-7182009-04-15RePEc:oup:biomet

article We study nonparametric likelihood-based estimators of the mean function of counting processes with panel count data using monotone polynomial splines. The generalized Rosen algorithm, proposed by Zhang & Jamshidian (2004), is used to compute the estimators. We show that the proposed spline likelihood-based estimators are consistent and that their rate of convergence can be faster than n-super-1/3. Simulation studies with moderate samples show that the estimators have smaller variances and mean squared errors than their alternatives proposed by Wellner & Zhang (2000). A real example from a bladder tumour clinical trial is used to illustrate this method. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 705 718 http://hdl.handle.net/10.1093/biomet/asm057 application/pdf Access to full text is restricted to subscribers. Minggen Lu Ying Zhang Jian Huang

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:149-1622009-04-15RePEc:oup:biomet

article In many modern experimental settings, observations are obtained in the form of functions and interest focuses on inferences about a collection of such functions. We propose a hierarchical model that allows us simultaneously to estimate multiple curves nonparametrically by using dependent Dirichlet process mixtures of Gaussian distributions to characterize the joint distribution of predictors and outcomes. Function estimates are then induced through the conditional distribution of the outcome given the predictors. The resulting approach allows for flexible estimation and clustering, while borrowing information across curves. We also show that the function estimates we obtain are consistent on the space of integrable functions. As an illustration, we consider an application to the analysis of conductivity and temperature at depth data in the north Atlantic. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 149 162 http://hdl.handle.net/10.1093/biomet/asn054 application/pdf Access to full text is restricted to subscribers. Abel Rodríguez David B. Dunson Alan E. Gelfand

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:760-7662009-04-15RePEc:oup:biomet

article High-dimension, low-small-sample size datasets have different geometrical properties from those of traditional low-dimensional data. In their asymptotic study regarding increasing dimensionality with a fixed sample size, Hall et al. (2005) showed that each data vector is approximately located on the vertices of a regular simplex in a high-dimensional space. A perhaps unappealing aspect of their result is the underlying assumption which requires the variables, viewed as a time series, to be almost independent. We establish an equivalent geometric representation under much milder conditions using asymptotic properties of sample covariance matrices. We discuss implications of the results, such as the use of principal component analysis in a high-dimensional space, extension to the case of nonindependent samples and also the binary classification problem. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 760 766 http://hdl.handle.net/10.1093/biomet/asm050 application/pdf Access to full text is restricted to subscribers. Jeongyoun Ahn J. S. Marron Keith M. Muller Yueh-Yun Chi

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:71-862009-04-15RePEc:oup:biomet

article We introduce a method based on a pseudolikelihood ratio for estimating the distribution function of the survival time in a mixed-case interval censoring model. In a mixed-case model, an individual is observed a random number of times, and at each time it is recorded whether an event has happened or not. One seeks to estimate the distribution of time to event. We use a Poisson process as the basis of a likelihood function to construct a pseudolikelihood ratio statistic for testing the value of the distribution function at a fixed point, and show that this converges under the null hypothesis to a known limit distribution, that can be expressed as a functional of different convex minorants of a two-sided Brownian motion process with parabolic drift. Construction of confidence sets then proceeds by standard inversion. The computation of the confidence sets is simple, requiring the use of the pool-adjacent-violators algorithm or a standard isotonic regression algorithm. We also illustrate the superiority of the proposed method over competitors based on resampling techniques or on the limit distribution of the maximum pseudolikelihood estimator, through simulation studies, and illustrate the different methods on a dataset involving time to <sc>HIV</sc> seroconversion in a group of haemophiliacs. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 71 86 http://hdl.handle.net/10.1093/biomet/asm011 application/pdf Access to full text is restricted to subscribers. Bodhisattva Sen Moulinath Banerjee

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:509-5132009-04-15RePEc:oup:biomet

article We describe an algorithm based upon the Sherman--Morrison--Woodbury formula for the inversion of matrices with special structure that occur in formulae for deletion diagnostics. Substantial computational savings relative to a method based upon Cholesky's decomposition are illustrated. The result has broad application to regression diagnostics for clustered data. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 509 513 http://hdl.handle.net/10.1093/biomet/asn019 application/pdf Access to full text is restricted to subscribers. John S. Preisser Bahjat F. Qaqish Jamie Perin

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:425-4462009-04-15RePEc:oup:biomet

article Probability kinematics (Jeffrey, 1965, 1983) furnishes a method for revising a prior probability specification based upon new probabilities over a partition. We develop a corresponding Bayes linear kinematic for a Bayes linear analysis given information which changes our beliefs about a random vector in some generalised way. We derive necessary and sufficient conditions for commutativity of successive Bayes linear kinematics which depend upon the eigenstructure of the joint kinematic resolution transform. As an application we introduce the Bayes linear Bayes graphical model, which is a mixture of fully Bayesian and Bayes linear graphical models, combining the simplicity of Gaussian graphical models with the ability to allow conditioning on marginal distributions of any form, and exploit Bayes linear kinematics to embed full conditional updates within Bayes linear belief adjustments. The theory is illustrated with a treatment of partition testing for software reliability. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 425 446 Michael Goldstein

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:911-9262009-04-15RePEc:oup:biomet

article In this paper we present an easy-to-implement graphical distribution diagnostic for linear models with correlated errors. Houseman et al. (2004) constructed quantile--quantile plots for the marginal residuals of such models, suitably transformed. We extend the pointwise asymptotic theory to address the global stochastic behaviour of the corresponding empirical cumulative distribution function, and describe a simulation technique that serves as a computationally efficient parametric bootstrap for generating representatives of its stochastic limit. Thus, continuous functionals of the empirical cumulative distribution function may be used to form global tests of normality. Through the use of projection matrices, we generalised our methods to include tests that are directed at assessing the normality of particular components of the error. Thus, tests proposed by Lange & Ryan (1989) follow as a special case. Our method works well both for models having independent units of sampling and for those in which all observations are correlated. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 911 926 http://hdl.handle.net/10.1093/biomet/93.4.911 text/html Access to full text is restricted to subscribers. E. Andres Houseman Brent A. Coull Louise M. Ryan

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:661-6722009-04-15RePEc:oup:biomet

article We illustrate how the recursive algorithm of Reeves & Pettitt (2004) for general factorizable models can be extended to allow exact sampling, maximization of distributions and computation of marginal distributions. All of the methods we describe apply to discrete-valued Markov random fields with nearest neighbour integrations defined on regular lattices; in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices. In this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as Markov chain Monte Carlo. In particular our work offers the basis for an automatic inference machine for such models. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 661 672 http://hdl.handle.net/10.1093/biomet/asm052 application/pdf Access to full text is restricted to subscribers. Nial Friel Håvard Rue

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:489-5072009-04-15RePEc:oup:biomet

article We develop diagnostic measures for assessing the influence of individual observations when using empirical likelihood with general estimating equations, and we use these measures to construct goodness-of-fit statistics for testing possible misspecification in the estimating equations. Our diagnostics include case-deletion measures, local influence measures and pseudo-residuals. Our goodness-of-fit statistics include the sum of local influence measures and the processes of pseudo-residuals. Simulation studies are conducted to evaluate our methods, and real datasets are analyzed to illustrate the use of our diagnostic measures and goodness-of-fit statistics. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 489 507 http://hdl.handle.net/10.1093/biomet/asm094 application/pdf Access to full text is restricted to subscribers. Hongtu Zhu Joseph G. Ibrahim Niansheng Tang Heping Zhang

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:419-4342009-04-15RePEc:oup:biomet

article In many applications of functional data analysis, summarising functional variation based on fits, without taking account of the estimation process, runs the risk of attributing the estimation variation to the functional variation, thereby overstating the latter. For example, the first eigenvalue of a sample covariance matrix computed from estimated functions may be biased upwards. We display a set of estimated neuronal Poisson-process intensity functions where this bias is substantial, and we discuss two methods for accounting for estimation variation. One method uses a random-coefficient model, which requires all functions to be fitted with the same basis functions. An alternative method removes the same-basis restriction by means of a hierarchical Gaussian process model. In a small simulation study the hierarchical Gaussian process model outperformed the randomcoefficient model and greatly reduced the bias in the estimated first eigenvalue that would result from ignoring estimation variability. For the neuronal data the hierarchical Gaussian process estimate of the first eigenvalue was much smaller than the naive estimate that ignored variability due to function estimation. The neuronal setting also illustrates the benefit of incorporating alignment parameters into the hierarchical scheme. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 419 434 http://hdl.handle.net/10.1093/biomet/92.2.419 text/html Access to full text is restricted to subscribers. Sam Behseta Robert E. Kass Garrick L. Wallstrom

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:207-2142009-04-15RePEc:oup:biomet

article A general class of semiparametric transformation models is studied for analysing survival data from the case-cohort design, which was introduced by Prentice (1986). Weighted estimating equations are proposed for simultaneous estimation of the regression parameters and the transformation function. It is shown that the resulting regression estimators are asymptotically normal, with variance-covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. Simulation studies show that the proposed approach is appropriate for practical use. An application to a case-cohort dataset from the Atherosclerosis Risk in Communities study is also given to illustrate the methodology. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 207 214 http://hdl.handle.net/10.1093/biomet/93.1.207 text/html Access to full text is restricted to subscribers. Wenbin Lu Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:591-6022009-04-15RePEc:oup:biomet

article We give several definitions of residual autocorrelations and derive their joint asymptotic distribution for the panel time series model of Hjellvik & Tjøstheim (1999a). A portmanteau goodness-of-fit test arises naturally from the asymptotic distribution. Simulation results show that the asymptotic standard errors compared satisfactorily with the empirical standard errors, that the goodness-of-fit test has reasonable empirical size, and that it is powerful enough to be useful with a modest sample size. The results of this paper are illustrated with a real-data example. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 591 602 Bo Fu

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:835-8482009-04-15RePEc:oup:biomet

article A class of semiparametric estimators are proposed in the general setting of functional measurement error models. The estimators follow from estimating equations that are based on the semiparametric efficient score derived under a possibly incorrect distributional assumption for the unobserved 'measured with error' covariates. It is shown that such estimators are consistent and asymptotically normal even with misspecification and are efficient if computed under the truth. The methods are demonstrated with a simulation study of a quadratic logistic regression model with measurement error. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 835 848 http://hdl.handle.net/10.1093/biomet/91.4.835 text/html Access to full text is restricted to subscribers. Anastasios A. Tsiatis Yanyuan Ma

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:679-7012009-04-15RePEc:oup:biomet

article Distributional theory regarding principal components is less well developed for correlation matrices than it is for covariance matrices. The intent of this paper is to reduce this disparity. Methods are proposed that enable investigators to fit and to make inferences about flexible principal components models for correlation matrices. The models allow arbitrary eigenvalue multiplicities and allow the distinct eigenvalues to be modelled parametrically or nonparametrically. Local parameterisations and implicit functions are used to construct full-rank unconstrained parameterisations. First-order asymptotic distributions are obtained directly from the theory of estimating functions. Second-order accurate distributions for making inferences under normality are obtained directly from likelihood theory. Simulation studies show that the Bartlett correction is effective in controlling the size of the tests and that first-order approximations to nonnull distributions are reasonably accurate. The methods are illustrated on a dataset. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 679 701 Robert J. Boik

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:605-6182009-04-15RePEc:oup:biomet

article Once treatment is found to be effective in clinical studies, attention often focuses on optimum or efficacious treatment delivery. In treatment duration-response studies, the optimum treatment delivery refers to the treatment length that optimises the mean response. In many studies, the treatment length is often left to the discretion of an attending investigator or physician but may be abruptly terminated because of treatment-terminating events. Thus, a recommended treatment length often delineates a 'treatment duration policy' which prescribes that treatment be given for a specified length of time or until a treatment-terminating event occurs, whichever comes first. Estimating a functional relationship between the response and a treatment duration policy, continuously in time, is the focus of this paper. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 605 618 http://hdl.handle.net/10.1093/biomet/92.3.605 text/html Access to full text is restricted to subscribers. Brent A. Johnson Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:579-5902009-04-15RePEc:oup:biomet

article This paper considers an extension of M-estimators in semiparametric models for independent observations to the case of longitudinal data. We approximate the nonparametric function by a regression spline, and any M-estimation algorithm for the usual linear models can then be used to obtain consistent estimators of the model and valid large-sample inferences about the regression parameters without any specification of the error distribution and the covariance structure. Included as special cases are the analysis of the conditional mean and median functions for longitudinal data. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 579 590 Xuming He

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:669-6782009-04-15RePEc:oup:biomet

article Given two sets of landmark data which differ in shape, it is useful to determine the extent to which shape variation can be explained by the perturbations of individual landmarks. We propose a method for assessing this, based on analysing the relative reduction in distance between the shapes that can be achieved by varying the location of a single landmark. This method is applied to a set of landmark data from the cervical vertebrae of two subspecies of gorillas. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 669 678 Michael H. Albert

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:785-8002009-04-15RePEc:oup:biomet

article Two methods of model selection are discussed for changepoint-like problems, especially those arising in genetic linkage analysis. The first is a method that selects the model with the smallest p-value, while the second is a modification of the Bayes information criterion. The methods are compared theoretically and on examples from the literature. For these examples, they are roughly comparable although the p-value-based method is somewhat more liberal in selecting a high-dimensional model. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 785 800 http://hdl.handle.net/10.1093/biomet/91.4.785 text/html Access to full text is restricted to subscribers. David Siegmund

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:389-3992009-04-15RePEc:oup:biomet

article In many biomedical studies, longitudinal count data comprise repeated responses and a set of multidimensional covariates for a large number of individuals. When the response variable in such models is subject to overdispersion, the overdispersion parameter influences the marginal variance. In such cases, the overdispersion parameter plays a significant role in efficient estimation of the regression parameters. This raises the need for joint estimation of the regression parameters and the overdispersion parameter, the longitudinal correlations being nuisance parameters. In this paper, we develop a generalised estimating equations approach based on a general autocorrelation structure for the repeated overdispersed data. The asymptotic properties of the estimators of the main parameters are discussed, and the estimation methodology is illustrated by analysing data on epileptic seizure counts. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 389 399 Vandna Jowaheer

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:507-5172009-04-15RePEc:oup:biomet

article For submodels of an exponential family, we consider likelihood ratio tests for hypotheses that render some parameters nonidentifiable. First, we establish the asymptotic equivalence between the likelihood ratio test and the score test. Secondly, the score-test representation is used to derive the asymptotic distribution of the likelihood ratio test. These results are derived for general submodels of an exponential family without assuming compactness of the parameter space. We then exemplify the results on a class of multivariate normal models, where null hypotheses concerning the covariance structure lead to loss of identifiability of a parameter. Our motivating problem throughout the paper is to test a random intercepts model against an alternative covariance structure allowing for serial correlation. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 507 517 http://hdl.handle.net/10.1093/biomet/92.3.507 text/html Access to full text is restricted to subscribers. Christian Ritz Ib M. Skovgaard

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:827-8412009-04-15RePEc:oup:biomet

article We consider parameter-driven models of time series of counts, where the observations are assumed to arise from a Poisson distribution with a mean changing over time according to a latent process. Estimation of these models is carried out within a Bayesian framework using data augmentation and Markov chain Monte Carlo methods. We suggest a new auxiliary mixture sampler, which possesses a Gibbsian transition kernel, where we draw from full conditional distributions belonging to standard distribution families only. Emphasis lies on application to state space modelling of time series of counts, but we show that auxiliary mixture sampling may be applied to a wider range of parameter-driven models, including random-effects models and panel data models based on the Poisson distribution. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 827 841 http://hdl.handle.net/10.1093/biomet/93.4.827 text/html Access to full text is restricted to subscribers. Sylvia FrüHwirth-Schnatter Helga Wagner

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:482-4882009-04-15RePEc:oup:biomet

article This paper contributes to the theory of Bayesian consistency for a sequence of posterior and predictive distributions arising from an independent and identically distributed sample. A new sufficient condition for posterior Hellinger consistency is presented which provides motivation for recent results appearing in the literature. Such motivation is important since current sufficient conditions are not known to be necessary. It also provides new insights into Bayesian consistency. A new consistency theorem for the sequence of predictive densities is given. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 482 488 Stephen Walker

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:283-3012009-04-15RePEc:oup:biomet

article When there are covariate effects to be considered, multi-state survival analysis is dominated either by parametric Markov regression models or by semiparametric Markov regression models using Cox's (1972) proportional hazards models for transition intensities between the states. The purpose of this research work is to study alternatives to Cox's model in a general finite-state Markov process setting. We shall look at two alternative models, Aalen's (1989) nonparametric additive hazards model and Lin & Ying's (1994) semiparametric additive hazards model. The former allows the effects of covariates to vary freely over time, while the latter assumes that the regression coefficients are constant over time. With the basic tools of the product integral and the functional delta-method, we present an estimator of the transition probability matrix and develop the large-sample theory for the estimator under each of these two models. Data on 1459 HLA identical sibling transplants for acute leukaemia from the International Bone Marrow Transplant Registry serve as illustration. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 283 301 http://hdl.handle.net/10.1093/biomet/92.2.283 text/html Access to full text is restricted to subscribers. Youyi Shu John P. Klein

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:742-7462009-04-15RePEc:oup:biomet

article Although Simes' modification of the Bonferroni procedure tends to perform very well, albeit often being slightly liberal for negatively dependent hypotheses, there are special cases where it fails more dramatically. We prove that these special cases are indeed special, applying only to specific significance levels, and obtain a strong bound on the average deviation of the Simes corrected P-value from the true probability over any interval of P-values. From this, it is argued that Simes' procedure should be expected to perform well except for pathological examples. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 742 746 http://hdl.handle.net/10.1093/biomet/93.3.742 text/html Access to full text is restricted to subscribers. Einar Andreas Rødland

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:717-7232009-04-15RePEc:oup:biomet

article Hierarchical likelihood provides a statistically efficient procedure for frailty models. Recently, a method using the computationally attractive orthodox best linear unbiased predictor has been proposed; this uses Pearson-type estimation. We compare both approaches and discuss their relative merits. With semiparametric frailty models difficulties can arise for the orthodox method, if the number of nuisance parameters increases with the sample size. This difficulty is avoided by the use of the hierarchical-likelihood method. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 717 723 http://hdl.handle.net/10.1093/biomet/92.3.717 text/html Access to full text is restricted to subscribers. Il Do Ha Youngjo Lee

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:577-5842009-04-15RePEc:oup:biomet

article Khmaladze-type goodness-of-fit tests are based on transforming an appropriate empirical process to one with a known large-sample distribution. Using Donsker's theorem, together with a theorem for proportional hazards generalising a theorem of Xu & O'Quigley (1999), we indicate how to construct a Khmaladze-type graphical test for evaluating the proportional hazards assumption. An illustration is given in which a partially proportional hazards model can be seen to provide a noticeably improved fit over a fully proportional hazards model. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 577 584 John O'Quigley

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:691-7032009-04-15RePEc:oup:biomet

article We investigate the variable selection problem for Cox's proportional hazards model, and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience. The new method is based on a penalized log partial likelihood with the adaptively weighted L₁ penalty on regression coefficients, providing what we call the adaptive Lasso estimator. The method incorporates different penalties for different coefficients: unimportant variables receive larger penalties than important ones, so that important variables tend to be retained in the selection process, whereas unimportant variables are more likely to be dropped. Theoretical properties, such as consistency and rate of convergence of the estimator, are studied. We also show that, with proper choice of regularization parameters, the proposed estimator has the oracle properties. The convex optimization nature of the method leads to an efficient algorithm. Both simulated and real examples show that the method performs competitively. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 691 703 http://hdl.handle.net/10.1093/biomet/asm037 application/pdf Access to full text is restricted to subscribers. Hao Helen Zhang Wenbin Lu

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:719-7332009-04-15RePEc:oup:biomet

article We propose a natural generalization of the Cox regression model, in which the regression coefficients have direct interpretations as temporal covariate effects on the survival function. Under the conditionally independent censoring mechanism, we develop a smoothing-free estimation procedure with a set of martingale-based equations. Our estimator is shown to be uniformly consistent and to converge weakly to a Gaussian process. A simple resampling method is proposed for approximating the limiting distribution of the estimated coefficients. Second-stage inferences with time-varying coefficients are developed accordingly. Simulations and a real example illustrate the practical utility of the proposed method. Finally, we extend this proposal of temporal covariate effects to the general class of linear transformation models and also establish a connection with the additive hazards model. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 719 733 http://hdl.handle.net/10.1093/biomet/asm058 application/pdf Access to full text is restricted to subscribers. Limin Peng Yijian Huang

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:45-632009-04-15RePEc:oup:biomet

article We propose a general Bayesian criterion for model assessment for categorical data called the weighted L measure, which is constructed from the posterior predictive distribution of the data. The measure is based on weighting the observations according to the sampling variance of their future response vector. The weight component in the weighted L measure plays the role of a penalty term in the criterion, in which a greater weight assigned to covariate values implies a greater penalty term on the dimension of the model. A detailed justification is provided for such a weighting procedure and several theoretical properties of the weighted L measure are presented for a wide variety of discrete data models. For these models, we examine properties of the weighted L measure, and show that it can perform better than the unweighted L measure in a variety of settings. In addition, we show that the weighted quadratic loss L measure is more attractive than the unweighted L measure and the deviance loss L measure for categorical data. Moreover, a calibration for the weighted L measure is motivated and proposed, which allows us to compare formally the L measure values of competing models. A detailed simulation study is presented to examine the performance of the weighted L measure, and it is compared to other established model-selection methods. Finally, the method is applied to a real dataset using a bivariate ordinal response model. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 45 63 Ming-Hui Chen

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:587-6032009-04-15RePEc:oup:biomet

article The accelerated failure time model is an attractive alternative to the Cox model when the proportionality assumption fails to capture the relationship between the survival time and longitudinal covariates. Several complications arise when the covariates are measured intermittently at different time points for different subjects, possibly with measurement errors, or measurements are not available after the failure time. Joint modelling of the failure time and longitudinal data offers a solution to such complications. We explore the joint modelling approach under the accelerated failure time assumption when covariates are assumed to follow a linear mixed effects model with measurement errors. The procedure is based on maximising the joint likelihood function with random effects treated as missing data. A Monte Carlo EM algorithm is used to estimate all the unknown parameters, including the unknown baseline hazard function. The performance of the proposed procedure is checked in simulation studies. A case study of reproductive egg-laying data for female Mediterranean fruit flies and their relationship to longevity demonstrate the effectiveness of the new procedure. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 587 603 http://hdl.handle.net/10.1093/biomet/92.3.587 text/html Access to full text is restricted to subscribers. Yi-Kuan Tseng Fushing Hsieh Jane-Ling Wang

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:1-222009-04-15RePEc:oup:biomet

article In two-group discriminant analysis, the Neyman--Pearson Lemma establishes that the ROC, receiver operating characteristic, curve for an arbitrary linear function is everywhere below the ROC curve for the true likelihood ratio. The weighted area between these two curves can be used as a risk function for finding good discriminant functions. The weight function corresponds to the objective of the analysis, for example to minimise the expected cost of misclassification, or to maximise the area under the ROC. The resulting discriminant functions can be estimated by iteratively reweighted logistic regression. We investigate some asymptotic properties in the 'near-logistic' setting, where we assume the covariates have been chosen such that a linear function gives a reasonable, but not necessarily exact, approximation to the true log likelihood ratio. Some examples are discussed, including a study of medical diagnosis in breast cytology. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 1 22 Shinto Eguchi

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:427-4412009-04-15RePEc:oup:biomet

article A key task in the elicitation of expert knowledge is to construct a distribution from the finite, and usually small, number of statements that have been elicited from the expert. These statements typically specify some quantiles or moments of the distribution. Such statements are not enough to identify the expert's probability distribution uniquely, and the usual approach is to fit some member of a convenient parametric family. There are two clear deficiencies in this solution. First, the expert's beliefs are forced to fit the parametric family. Secondly, no account is then taken of the many other possible distributions that might have fitted the elicited statements equally well. We present a nonparametric approach which tackles both of these deficiencies. We also consider the issue of the imprecision in the elicited probability judgements. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 427 441 http://hdl.handle.net/10.1093/biomet/asm031 application/pdf Access to full text is restricted to subscribers. Jeremy E. Oakley Anthony O'Hagan

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:619-6322009-04-15RePEc:oup:biomet

article The accelerated failure time model specifies that the logarithm of the failure time is linearly related to the covariate vector without assuming a parametric error distribution. In this paper, we consider the semiparametric Box--Cox transformation model, which includes the above regression model as a special case, to analyse possibly censored failure time observations. Inference procedures for the transformation and regression parameters are proposed via a resampling technique. Prediction of the survival function of future subjects with a specific covariate vector is also provided via pointwise and simultaneous interval estimates. All the proposals are illustrated with datasets from two clinical studies. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 619 632 http://hdl.handle.net/10.1093/biomet/92.3.619 text/html Access to full text is restricted to subscribers. Tianxi Cai Lu Tian L. J. Wei

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:859-8742009-04-15RePEc:oup:biomet

article We consider Bayesian inference about collections of unknown distributions subject to a partial stochastic ordering. To address problems in testing of equalities between groups and estimation of group-specific distributions, we propose classes of restricted dependent Dirichlet process priors. These priors have full support in the space of stochastically ordered distributions, and can be used for collections of unknown mixture distributions to obtain a flexible class of mixture models. Theoretical properties are discussed, efficient methods are developed for posterior computation using Markov chain Monte Carlo simulation and the methods are illustrated using data from a study of DNA damage and repair. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 859 874 http://hdl.handle.net/10.1093/biomet/asn043 application/pdf Access to full text is restricted to subscribers. David B. Dunson Shyamal D. Peddada

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:661-6812009-04-15RePEc:oup:biomet

article Motivated by two practical problems, we propose a new procedure for estimating a semivarying-coefficient model. Asymptotic properties are established which show that the bias of the parameter estimator is of order h-super-3 when a symmetric kernel is used, where h is the bandwidth, and the variance is of order n-super- - 1 and efficient in the semiparametric sense. Undersmoothing is unnecessary for the root-n consistency of the estimators. Therefore, commonly used bandwidth selection methods can be employed. A model selection method is also developed. Simulations demonstrate how the proposed method works. Some insights are obtained into the two motivating problems by using the proposed models. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 661 681 Yingcun Xia

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:230-2372009-04-15RePEc:oup:biomet

article <?Pub Caret> Design weights in surveys are often adjusted to accommodate auxiliary information and to meet pre-specified range restrictions, typically via some ad hoc algorithmic adjustment to a generalised regression estimator. In this paper, we present a simple solution to this problem using empirical likelihood methods or generalised regression. We first develop algorithms for computing empirical likelihood estimators and model-calibrated empirical likelihood estimators. The first algorithm solves the computational problem of the empirical likelihood method in general, both in survey and non-survey settings, and theoretically guarantees its convergence. The second exploits properties of the model-calibration method and is particularly simple. The algorithms are adapted for handling benchmark constraints and pre-specified range restrictions on the weight adjustments. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 230 237 J. Chen

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:437-4502009-04-15RePEc:oup:biomet

article This paper concerns high-order inference for scalar parameters that are estimated by functions of multivariate M-estimators. Asymptotic formulae for the bias and skewness of the studentised statistic are derived. Although these formulae appear complicated, they can be evaluated easily by using matrix operations and numerical differentiation. Various methods for constructing second-order accurate confidence limits are discussed, including a method based on skewness-reducing transformations and a generalisation of the ABC method. The use of the skewness-reducing transformations is closely related to empirical likelihood; expressing the studentised statistic in terms of a skewness-reducing reparameterisation brings the standard asymptotic intervals closer in shape to empirical likelihood intervals. The improvement in one- and two-sided coverage accuracy achieved by taking the bias and skewness into account is illustrated in numerical examples. It is found in the examples that taking skewness into account by reparameterisation or parameterisation invariance yields better coverage accuracy than correcting for skewness by polynomial expansions. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 437 450 Thomas J. DiCiccio

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:179-1952009-04-15RePEc:oup:biomet

article We propose a shrinkage estimator for spectral densities based on a multilevel normal hierarchical model. The first level captures the sampling variability via a likelihood constructed using the asymptotic properties of the periodogram. At the second level, the spectral density is shrunk towards a parametric time series model. To avoid selecting a particular parametric model for the second level, a third level is added which induces an estimator that averages over a class of parsimonious time series models. The estimator derived from this model, the model averaged shrinkage estimator, is consistent, is shown to be highly competitive with other spectral density estimators via simulations, and is computationally inexpensive. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 179 195 http://hdl.handle.net/10.1093/biomet/93.1.179 text/html Access to full text is restricted to subscribers. Carsten H. Botts Michael J. Daniels

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:905-9162009-04-15RePEc:oup:biomet

article We consider the problem of matched studies with a binary outcome that are analysed using conditional logistic regression, and for which data on some covariates are missing for some study participants. Methods for this problem involve either modelling the distribution of missing covariates or modelling the probability of data being missing. For this second approach, the previously proposed method did not make use of data for those persons with missing covariate data except in the model for the missingness. We propose a new class of estimators that use outcome and available covariate data for all study participants, and show that a particular member of this class always has better efficiency than the previously proposed estimator. We illustrate the efficiency gains that are possible with our approach using simulated data. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 905 916 Paul J. Rathouz

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:755-7592009-04-15RePEc:oup:biomet

article A relationship due to W.G. Cochran showing the effect on least squares regression coefficients of marginalizing over or conditioning on an explanatory variable is generalized to quantile regression coefficients. The condition under which conditioning does not induce interaction or effect reversal is shown. Examples are given. The discussion is simplest when all variables are continuous; the extension to discrete variables is outlined. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 755 759 http://hdl.handle.net/10.1093/biomet/asm046 application/pdf Access to full text is restricted to subscribers. D. R. Cox

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:486-4892009-04-15RePEc:oup:biomet

article In this note we give an alternative formulation of the nonparametric estimators of Wang (2003) with the identity link. This results in a closed form of the estimator that has computational advantages and gives insight into the rationale behind the estimator. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 486 489 http://hdl.handle.net/10.1093/biomet/93.2.486 text/html Access to full text is restricted to subscribers. Richard Huggins

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:819-8342009-04-15RePEc:oup:biomet

article We extend the idea of crossvalidation to choose the smoothing parameters of the 'double-kernel' local linear regression for estimating a conditional density. Our selection rule optimises the estimated conditional density function by minimising the integrated squared error. We also discuss three other bandwidth selection rules, an ad hoc method used by Fan et al. (1996), a bootstrap method of Hall et al. (1999) for bandwidth selection in the estimation of conditional distribution functions, modified by Bashtannyk & Hyndman (2001) to cover conditional density functions, and finally a simple approach proposed by Hyndman & Yao (2002). The performance of the new approach is compared with these three methods by simulation studies, and our method performs outstandingly well. The method is illustrated by an application to estimating the transition density and the Value-at-Risk of treasury-bill data. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 819 834 http://hdl.handle.net/10.1093/biomet/91.4.819 text/html Access to full text is restricted to subscribers. Jianqing Fan Tsz Ho Yim

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:917-9312009-04-15RePEc:oup:biomet

article In many clinical trials for evaluating treatment efficacy, it is believed that there may exist latent treatment effectiveness lag times after which medical treatment procedure or chemical compound would be in full effect. In this paper, semiparametric regression models are proposed and studied for estimating the treatment effect accounting for such latent lag times. The new models take advantage of the invariant property of the additive hazards model in marginalising over an additive latent variable; parameters in the models are thus easily estimated and interpreted, while the flexibility of not having to specify the baseline hazard function is preserved. Monte Carlo simulation studies demonstrate the appropriateness of the proposed semiparametric estimation procedure. The methodology is applied to data collected in a randomised clinical trial, which evaluates the efficacy of biodegradable carmustine polymers for treatment of recurrent brain tumours. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 917 931 Y. Q. Chen

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:459-4642009-04-15RePEc:oup:biomet

article We consider rank-based regression models for repeated measures. To account for possible withinsubject correlations, we decompose the total ranks into between- and within-subject ranks and obtain two different estimators based on between- and within-subject ranks. A simple perturbation method is then introduced to generate bootstrap replicates of the estimating functions and the parameter estimates. This provides a convenient way for combining the corresponding two types of estimating function for more efficient estimation. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 459 464 http://hdl.handle.net/10.1093/biomet/93.2.459 text/html Access to full text is restricted to subscribers. You-Gan Wang Min Zhu

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:65-802009-04-15RePEc:oup:biomet

article In statistical models of dependence, the effect of a categorical variable is typically described by contrasts among parameters. For reporting such effects, quasi-variances provide an economical and intuitive method which permits approximate inference on any contrast by subsequent readers. Applications include generalised linear models, generalised additive models and hazard models. The present paper exposes the generality of quasi-variances, emphasises the need to control relative errors of approximation, gives simple methods for obtaining quasi-variances and bounds on the approximation error involved, and explores the domain of accuracy of the method. Conditions are identified under which the quasi-variance approximation is exact, and numerical work indicates high accuracy in a variety of settings. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 65 80 David Firth

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:457-4612009-04-15RePEc:oup:biomet

article Structural vector autoregressions allow contemporaneous series dependence and assume errors with no contemporaneous correlation. Models of this form, that also have a recursive structure, can be described by a directed acyclic graph. An important tool for identification of these models is the conditional independence graph constructed from the contemporaneous and lagged values of the process. We determine the large-sample properties of statistics used to test for the presence of links in this graph. A simple example illustrates how these results may be applied. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 457 461 Marco Reale

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:841-8502009-04-15RePEc:oup:biomet

article We address the matter of determining whether or not missing data in longitudinal studies are ignorable with regard to quasilikelihood or estimating equations approaches. This involves testing for whether or not the zero-mean property of estimating equations holds true. Chen & Little (1999) proposed testing for significant differences among parameter estimators calculated from sample subsets with different patterns of missing data, whereas we propose a more unified generalised score-type test. This avoids exhaustive estimation of parameters for each missing-data pattern, testing instead with a single quadratic score test statistic whether or not there is a common parameter under which the means of all the pattern-specific estimating equations are zero. Comparisons are made for the two approaches with both simulations and real data examples. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 841 850 Annie Qu

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:673-6892009-04-15RePEc:oup:biomet

article Optimal decision-analytic designs are deterministic. Such designs are appropriately criticized in the context of clinical trials because they are subject to assignment bias. On the other hand, balanced randomized designs may assign an excessive number of patients to a treatment arm that is performing relatively poorly. We propose a compromise between these two extremes, one that achieves some of the good characteristics of both. We introduce a constrained optimal adaptive design for a fully sequential randomized clinical trial with k arms and n patients. An r-design is one for which, at each allocation, each arm has probability at least r of being chosen, 0 ⩽ r ⩽ 1/k. An optimal design among all r-designs is called r-optimal. An r₁-design is also an r₂-design if r₁ ⩾ r₂. A design without constraint is the special case r = 0 and a balanced randomized design is the special case r = 1/k. The optimization criterion is to maximize the expected overall utility in a Bayesian decision-analytic approach, where utility is the sum over the utilities for individual patients over a 'patient horizon' N. We prove analytically that there exists an r-optimal design such that each patient is assigned to a particular one of the arms with probability 1 − (k − 1)r, and to the remaining arms with probability r. We also show that the balanced design is asymptotically r-optimal for any given r, 0 ⩽ r < 1/k, as N/n → ∞. This implies that every r-optimal design is asymptotically optimal without constraint. Numerical computations using backward induction for k = 2 arms show that, in general, this asymptotic optimality feature for r-optimal designs can be accomplished with moderate trial size n if the patient horizon N is large relative to n. We also show that, in a trial with an r-optimal design, r < 1/2, fewer patients are assigned to an inferior arm than when following a balanced design, even for r-optimal designs having the same statistical power as a balanced design. We discuss extensions to various clinical trial settings. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 673 689 http://hdl.handle.net/10.1093/biomet/asm049 application/pdf Access to full text is restricted to subscribers. Yi Cheng Donald A. Berry

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:461-4702009-04-15RePEc:oup:biomet

article The Robbins--Monro procedure does not perform well in the estimation of extreme quantiles, because the procedure is implemented using asymptotic results, which are not suitable for binary data. Here we propose a modification of the Robbins--Monro procedure and derive the optimal procedure for binary data under some reasonable approximations. The improvement obtained by using the optimal procedure for the estimation of extreme quantiles is substantial. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 461 470 V. Roshan Joseph

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:471-4902009-04-15RePEc:oup:biomet

article We propose a method for finding the alternative distribution in importance sampling. The alternative distribution is optimal in the sense that the asymptotic variance is minimised for estimating tail probabilities of asymptotically normal statistics. Our contribution to importance sampling is three-fold. To begin with, we obtain an explicit expression for the mean of the optimal alternative distribution and the expression motivates a recursive approximation algorithm. Secondly, a new multi-dimensional exponential tilting formula is presented. Lastly, a conservative estimator of the variance is given to facilitate a quick comparison among different stratified sampling schemes in conjunction with importance sampling. Several numerical examples illustrating the efficacy of the proposed method are also included. These results indicate that the proposed method is considerably more efficient than the method based on large deviations theory and the efficiency gain is more significant in higher dimensions. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 471 490 Cheng-Der Fuh

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:703-7162009-04-15RePEc:oup:biomet

article We consider the testing and estimation of thresholds in heteroscedastic threshold autoregressive models with an unknown number of thresholds. A test statistic based on empirical wavelet coefficients is proposed. The asymptotic distribution of the test statistic is established and consistent estimators of the thresholds and the number of thresholds are given. A Monte Carlo study and a real example are used to assess the performance of our method. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 703 716 Wai-Cheung Ip

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:647-6592009-04-15RePEc:oup:biomet

article We introduce and exemplify an efficient method for direct sampling from hyper-inverse Wishart distributions. The method relies very naturally on the use of standard junction-tree representation of graphs, and couples these with matrix results for inverse Wishart distributions. We describe the theory and resulting computational algorithms for both decomposable and nondecomposable graphical models. An example drawn from financial time series demonstrates application in a context where inferences on a structured covariance model are required. We discuss and investigate questions of scalability of the simulation methods to higher-dimensional distributions. The paper concludes with general comments about the approach, including its use in connection with existing Markov chain Monte Carlo methods that deal with uncertainty about the graphical model structure. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 647 659 http://hdl.handle.net/10.1093/biomet/asm056 application/pdf Access to full text is restricted to subscribers. Carlos M. Carvalho Hélène Massam Mike West

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:617-6342009-04-15RePEc:oup:biomet

article We present a method for estimating the survival curve of a continuous failure time random variable from right-censored data. Our method allows adjustment for informative censoring due to measured prognostic factors for time-to-event and censoring while simultaneously quantifying the sensitivity of the inference to residual dependence between failure and censoring due to unmeasured factors. We present the results of a simulation study and illustrate our approach using data from the AIDS Clinical Trial Group 175 study. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 617 634 Daniel O. Scharfstein

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:603-6162009-04-15RePEc:oup:biomet

article A simulation smoother in state space time series analysis is a procedure for drawing samples from the conditional distribution of state or disturbance vectors given the observations. We present a new technique for this which is both simple and computationally efficient. The treatment includes models with diffuse initial conditions and regression effects. Computational comparisons are made with the previous standard method. Two applications are provided to illustrate the use of the simulation smoother for Gibbs sampling for Bayesian inference and importance sampling for classical inference. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 603 616 J. Durbin

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:447-4592009-04-15RePEc:oup:biomet

article In the presence of data contamination or outliers, some empirical studies have indicated that the two methods of generalised estimating equations and quadratic inference functions appear to have rather different robustness behaviour. This paper presents a theoretical investigation from the perspective of the influence function to identify the causes for the difference. We show that quadratic inference functions lead to bounded influence functions and the corresponding M-estimator has a redescending property, but the generalised estimating equation approach does not. We also illustrate that, unlike generalised estimating equations, quadratic inference functions can still provide consistent estimators even if part of the data is contaminated. We conclude that the quadratic inference function is a preferable method to the generalised estimating equation as far as robustness is concerned. This conclusion is supported by simulations and real-data examples. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 447 459 Annie Qu

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:997-10012009-04-15RePEc:oup:biomet

article Necessary and sufficient conditions for consistency of a simple estimator of Kendall's tau under bivariate censoring are presented. The results are extended to data subject to bivariate left truncation as well as right censoring. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 997 1001 http://hdl.handle.net/10.1093/biomet/asn037 application/pdf Access to full text is restricted to subscribers. David Oakes

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:767-7672009-04-15RePEc:oup:biomet

article The left-hand side of equation (2·8), on p. 671, should read {π₁ (1 − π₁)}-super-−1/2 (2π₁ − 1) rather than {(1 − π₁)/π₁}-super-1/2 (2π₁ − 1). Reflecting this change, the left-hand side of equation (3·1) on the same page should be altered to <inline-formula><mml:math><mml:mrow><mml:mo stretchy="false">{</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mo ver><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>Ȣ 7;</mml:mi></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn>< /mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml :msub><mml:mrow><mml:mover><mml:mrow><mml:mi>π</mml:mi></mml:mrow>< mml:mrow><mml:mi>∧</mml:mi></mml:mrow></mml:mover></mml:mrow><mml:m row><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">}</mml:mo></mml:mrow><mml:mrow><mml:mo>−</mml:mo>< mml:mn>1/2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mrow><mml:move r><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>∧ </mml:mi></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn></m ml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula>, and the formula at the foot of p. 677 should be modified to {π₁ (1 − π₁)}-super-−1/2 (2π₁ − 1) + O_p(n-super-−1/2). No other formula is affected, and the left-hand side of (2·8) is still increasing in π₁. The numerical results, discussed in §4, are influenced in minor ways. In the simulation study, absolute bias is reduced, and variance is either slightly increased or slightly decreased. In the real-data example, using the nonparametric approach to analysis, mean squared error is further reduced, from 0·0011 to 0·0004. We are grateful to Hiro Kasahara and Katsumi Shimotsu for pointing out the error. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 767 767 http://hdl.handle.net/10.1093/biomet/asm042 application/pdf Access to full text is restricted to subscribers. Peter Hall Amnon Neeman Reza Pakyari Ryan Elmore

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:943-9592009-04-15RePEc:oup:biomet

article We consider a model-dependent approach for multi-level modelling that accounts for informative probability sampling of first- and lower-level population units. The proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample, as a function of the corresponding population model and the first- and lower-level sample selection probabilities, and then fitting the resulting sample model using Bayesian methods. An important implication of the use of the model holding for the sample is that the sample selection probabilities feature in the analysis as additional data that possibly strengthen the estimators. A simulation experiment is carried out in order to study the performance of this approach and compare it to the use of 'design-based' methods. The simulation study indicates that both approaches perform in general equally well in terms of point estimation, but the model-dependent approach yields confidence/credibility intervals with better coverage properties. Another simulation study assesses the impact of misspecification of the models assumed for the sample selection probabilities. The use of maximum likelihood estimation is also considered. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 943 959 http://hdl.handle.net/10.1093/biomet/93.4.943 text/html Access to full text is restricted to subscribers. Danny Pfeffermann Fernando Antonio Da Silva Moura Pedro Luis Do Nascimento Silva

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:573-5862009-04-15RePEc:oup:biomet

article This paper considers the analysis of current status data with a cured proportion in the population using a mixture model that combines a logistic regression formulation for the probability of cure with a semiparametric regression model for the time to occurrence of the event. The semiparametric regression model belongs to the flexible class of partly linear models that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies were carried out to investigate the performance of the proposed method and the model is fitted to a dataset from a study of calcification of the hydrogel intraocular lenses, a complication of cataract treatment. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 573 586 http://hdl.handle.net/10.1093/biomet/92.3.573 text/html Access to full text is restricted to subscribers. K. F. Lam Hongqi Xue

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:303-3162009-04-15RePEc:oup:biomet

article In this paper, we propose a penalised pseudo-partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients. Under certain regularity conditions, we show the consistency and asymptotic normality of the penalised likelihood estimators. We further demonstrate that, for certain penalty functions with proper choices of regularisation parameters, the resulting estimator can correctly identify the true model, as if it were known in advance. Based on a simple approximation of the penalty function, the proposed method can be easily carried out with the Newton--Raphson algorithm. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed procedures. We illustrate the proposed method by analysing a dataset from the Framingham Heart Study. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 303 316 http://hdl.handle.net/10.1093/biomet/92.2.303 text/html Access to full text is restricted to subscribers. Jianwen Cai Jianqing Fan Runze Li Haibo Zhou

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:559-5712009-04-15RePEc:oup:biomet

article Modelling human genetic variation is critical to understanding the genetic basis of complex disease. The Human Genome Project has discovered millions of binary DNA sequence variants, called single nucleotide polymorphisms, and millions more may exist. As coding for proteins takes place along chromosomes, organisation of polymorphisms along each chromosome, the haplotype phase structure, may prove to be most important in discovering genetic variants associated with disease. As haplotype phase is often uncertain, procedures that model the distribution of parental haplotypes can, if this distribution is misspecified, lead to substantial bias in parameter estimates even when complete genotype information is available. Using a geometric approach to estimation in the presence of nuisance parameters, we address this problem and develop locally-efficient estimators of the effect of haplotypes on disease that are robust to incorrect estimates of haplotype frequencies. The methods are demonstrated with a simulation study of a case-parent design. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 559 571 http://hdl.handle.net/10.1093/biomet/92.3.559 text/html Access to full text is restricted to subscribers. Andrew S. Allen Glen A. Satten Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:307-3232009-04-15RePEc:oup:biomet

article We propose a class of kernel stick-breaking processes for uncountable collections of dependent random probability measures. The process is constructed by first introducing an infinite sequence of random locations. Independent random probability measures and beta-distributed random weights are assigned to each location. Predictor-dependent random probability measures are then constructed by mixing over the locations, with stick-breaking probabilities expressed as a kernel multiplied by the beta weights. Some theoretical properties of the process are described, including a covariate-dependent prediction rule. A retrospective Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using a simulated example and an epidemiological application. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 307 323 http://hdl.handle.net/10.1093/biomet/asn012 application/pdf Access to full text is restricted to subscribers. David B. Dunson Ju-Hyun Park

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:649-6582009-04-15RePEc:oup:biomet

article Current status data arise when the exact timing of an event is unobserved, and it is only known at a given point in time whether or not the event has occurred. Recently Lin et al. (1998) studied the additive semiparametric hazards model for current status data. They showed that the analysis of current status data under the additive hazards model reduces to ordinary Cox regression under the assumption that a proportional hazards model may be used to describe the monitoring intensity. This analysis does not make efficient use of data, and in some cases it may not be appropriate to assume a proportional hazards model for the monitoring times. We study the semiparametric hazards model for current status data but make use of the semiparametric efficient score function. The suggested approach has the advantages that it is efficient in that it reaches the semiparametric information bound, and it does not involve any modelling of the monitoring times. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 649 658 Torben Martinussen

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:732-7362009-04-15RePEc:oup:biomet

article We derive a Monte-Carlo-amenable, minimum variance unbiased estimator of a nonlinear function of a normal mean and the variance of the estimator. Applications to problems arising in the analysis of data measured with error are described. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 732 736 http://hdl.handle.net/10.1093/biomet/92.3.732 text/html Access to full text is restricted to subscribers. Leonard A. Stefanski Steven J. Novick Viswanath Devanarayan

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:569-5842009-04-15RePEc:oup:biomet

article Regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields. Sufficient dimension reduction provides a promising approach to such problems, by restricting attention to d < n linear combinations of the original p predictors. However, standard methods of sufficient dimension reduction require inversion of the sample predictor covariance matrix. We propose a method for estimating the central subspace that eliminates the need for such inversion and is applicable regardless of the (n, p) relationship. Simulations show that our method compares favourably with standard large sample techniques when the latter are applicable. We illustrate our method with a genomics application. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 569 584 http://hdl.handle.net/10.1093/biomet/asm038 application/pdf Access to full text is restricted to subscribers. R. Dennis Cook Bing Li Francesca Chiaromonte

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:491-4962009-04-15RePEc:oup:biomet

article In regression problems it is hard to detect correlated errors since the errors are not observed. In this paper, a nonparametric method is proposed for the detection of correlated errors when the design points are equally spaced. It turns out that the first-order sample autocovariance of the residuals from the kernel regression estimates provides essential information about correlated errors and its bootstrap is quite effective in implementing such information. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 491 496 Tae Yoon Kim

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:509-5112009-04-15RePEc:oup:biomet

article This note presents a direct adjustment of the estimative prediction limit to reduce the coverage error from a target value to third-order accuracy. The adjustment is asymptotically equivalent to those of Barndorff-Nielsen & Cox (1994, 1996) and Vidoni (1998). It has a simpler form with a plug-in estimator of the coverage probability of the estimative limit at the target value. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 509 511 http://hdl.handle.net/10.1093/biomet/asm032 application/pdf Access to full text is restricted to subscribers. Masao Ueki Kaoru Fueda

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:285-2962009-04-15RePEc:oup:biomet

article We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared distributions in general. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 285 296 http://hdl.handle.net/10.1093/biomet/asm021 application/pdf Access to full text is restricted to subscribers. Yongwu Shao R. Dennis Cook Sanford Weisberg

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:163-1772009-04-15RePEc:oup:biomet

article Two-stage randomisation designs are useful in the evaluation of combination therapies where patients are initially randomised to an induction therapy and then, depending upon their response and consent, are randomised to a maintenance therapy. In this paper we derive the best regular asymptotically linear estimator for the survival distribution and related quantities of treatment regimes. We propose an estimator which is easily computable and is more efficient than existing estimators. Large-sample properties of the proposed estimator are derived and comparisons with other estimators are made using simulation. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 163 177 http://hdl.handle.net/10.1093/biomet/93.1.163 text/html Access to full text is restricted to subscribers. Abdus S. Wahed Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:519-5282009-04-15RePEc:oup:biomet

article A composite likelihood consists of a combination of valid likelihood objects, usually related to small subsets of data. The merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models, even when the use of standard likelihood or Bayesian methods is not feasible. In this paper, we aim to suggest an integrated, general approach to inference and model selection using composite likelihood methods. In particular, we introduce an information criterion for model selection based on composite likelihood. We also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well-known Old Faithful geyser dataset. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 519 528 http://hdl.handle.net/10.1093/biomet/92.3.519 text/html Access to full text is restricted to subscribers. Cristiano Varin Paolo Vidoni

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:265-2812009-04-15RePEc:oup:biomet

article We introduce a class of Bayesian semiparametric models for regression problems in which the response variable is a count. Our goal is to provide a flexible, easy-to-implement and robust extension of generalised linear models, for datasets of moderate or large size. Our approach is based on modelling the distribution of the response variable using a Dirichlet process, whose mean distribution function is itself random and is given a parametric form, such as a generalised linear model. The effects of the explanatory variables on the response are modelled via both the parameters of the mean distribution function of the Dirichlet process and the total mass parameter. We discuss modelling options and relationships with other approaches. We derive in closed form the marginal posterior distribution of the regression coefficients and discuss its use in inference and computing. We illustrate the benefits of our approach with a prognostic model for early breast cancer patients. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 265 281 Cinzia Carota

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:451-4562009-04-15RePEc:oup:biomet

article The paper presents a method for estimating nonparametrically the states of one-dimensional diffusion processes. Once certain nuisance parameters have been estimated from the time series, states of a diffusion process can be estimated by the Kalman filter algorithm, so that the method is also useful for filtering and smoothing the states of the process. Numerical comparison of the method with the case of fitting a linear model to data shows that the method is clearly superior in terms of prediction errors. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 451 456 Isao Shoji

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:343-3552009-04-15RePEc:oup:biomet

article When treatment effects are studied in the context of successive or recurrent life events, separate analyses of the quality-of-life scores and of the inter-event, gap, times might lead to possibly contradictory conclusions. In an attempt to reconcile this, we propose a unitary and more comprehensive nonparametric analysis that combines the two separate analyses by introducing the quality-of-life-adjusted gap time concept. Inverse probability of censoring estimators of the quality-of-life-adjusted gap time joint and conditional distributions are proposed and are shown to be consistent and asymptotically normal. Simulations performed in a variety of scenarios indicate that the joint and conditional quality-of-life-adjusted gap time distribution estimators are virtually unbiased, with properly estimated standard errors and asymptotic normality features. An example from the International Breast Cancer Study Group Trial V illustrates the use of the proposed estimators. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 343 355 http://hdl.handle.net/10.1093/biomet/93.2.343 text/html Access to full text is restricted to subscribers. Adin-Cristian Andrei Susan Murray

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:238-2442009-04-15RePEc:oup:biomet

article We propose a method for comparing survival distributions when cause-of-failure information is missing for some individuals. We use multiple imputation to impute missing causes of failure, where the probability that a missing cause is that of interest may depend on auxiliary covariates, and combine log-rank statistics computed from several 'completed' datasets into a test statistic that achieves asymptotically the nominal level. Simulations demonstrate the relevance of the theory in finite samples. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 238 244 Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:435-4502009-04-15RePEc:oup:biomet

article Most methods for analysing cluster-correlated biological data implicitly assume the ignorability of cluster sizes. When this assumption fails, the resulting inferences may be asymptotically invalid. Hoffman et al. (2001) proposed a simple but computationally intensive method, based on a large number of within-cluster resamples and associated separate estimating equations, that leads to asymptotically valid inferences whether the cluster sizes are ignorable or not. We study a simple method, based on a single inverse cluster size-weighted estimating equation, that avoids resampling and yet leads to asymptotically valid inferences. Simulation results are presented to assess the performance of the proposed method. We also propose Wald tests for ignorability of cluster sizes. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 435 450 http://hdl.handle.net/10.1093/biomet/92.2.435 text/html Access to full text is restricted to subscribers. E. Benhin J. N. K. Rao A. J. Scott

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:585-6012009-04-15RePEc:oup:biomet

article Sliced inverse regression, sliced inverse regression II and sliced average variance estimation are three related dimension-reduction methods that require relatively mild model assumptions. As an approximation for the relative influence of single observations from large samples, the influence function is used to compare the sensitivity of the three methods to particular observational types. The analysis carried out here helps to explain why there is a lack of agreement concerning the preferability of these dimension-reduction procedures in general. An efficient sample version of the influence function is also developed and evaluated. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 585 601 http://hdl.handle.net/10.1093/biomet/asm055 application/pdf Access to full text is restricted to subscribers. Luke A. Prendergast

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:923-9362009-04-15RePEc:oup:biomet

article Consider designing a clinical trial in stages, with two treatments and N exchangeable patients to be treated. Responses are dichotomous. The problem is to decide how large each stage should be and how many patients should be assigned to each treatment during each stage. Information is updated during and after each stage using Bayes' theorem. In planning stage j, responses from selections in stages 1 to j - 1 are available, but interim responses in stage j are not available. Our analytical results consider two stages for two scenarios, when one treatment arm is known and when both treatment arms are unknown. The dominant term for the length of the first stage in an optimal design for general N is found explicitly. In both scenarios the order of magnitude of the length of the first stage is the square root of N. The finite-N performance of asymptotically optimal allocation is compared with that of the true optimal allocation. Our numerical study also shows that, for a trial of three stages with one known arm, the optimal first-stage sample size is asymptotically proportional to the cube root of N. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 923 936 Yi Cheng

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:119-1342009-04-15RePEc:oup:biomet

article A local likelihood estimator for a nonparametric nuisance function is proposed in the context of semiparametric skew-normal distributions. Constraints imposed on such functions result in a nonparametric estimator with a different target function for maximization from classical local likelihood estimators. The optimal asymptotic semiparametric efficiency bound on parameters of interest is achieved by using this estimator in conjunction with an estimating equation formed by summing efficient scores. A generalized profile likelihood approach is also proposed. This method has the advantage of providing a unique estimate in cases where an estimating equation has multiple solutions. Our nonparametric estimator of the nuisance function leads to an estimator of the semiparametric skew-normal density. Both the estimating equation and profile likelihood approaches are applicable to more general skew-symmetric distributions. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 119 134 http://hdl.handle.net/10.1093/biomet/asm020 application/pdf Access to full text is restricted to subscribers. Yanyuan Ma Jeffrey D. Hart

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:819-8292009-04-15RePEc:oup:biomet

article We introduce a method for estimating nonstationary spatial covariance structure from space-time data and apply the method to an analysis of Sydney wind patterns. Our method constructs a process honouring a given spatial covariance matrix at observing stations and uses one or more stationary processes to describe conditional behaviour given observing site values. The stationary processes give a localised description of the spatial covariance structure. The method is computationally attractive, and can be extended to the assessment of covariance for multivariate processes. The technique is illustrated for data describing the east-west component of Sydney winds. For this example, our own methods are contrasted with a geometrically appealing though computationally intensive technique which describes spatial correlation via an isotropic process and a deformation of the geographical space. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 819 829 David J. Nott

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:472-4802009-04-15RePEc:oup:biomet

article Two existing density estimators based on local likelihood have properties that are comparable to those of local likelihood regression but they are much less used than their counterparts in regression. We consider truncation as a natural way of localising parametric density estimation. Based on this idea, a third local likelihood density estimator is introduced. Our main result establishes that the three estimators coincide when a free multiplicative constant is used as an extra local parameter. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 472 480 http://hdl.handle.net/10.1093/biomet/93.2.472 text/html Access to full text is restricted to subscribers. Pedro Delicado

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:801-8182009-04-15RePEc:oup:biomet

article Marginal additive hazards models are considered for multivariate survival data in which individuals may experience events of several types and there may also be correlation between individuals. Estimators are proposed for the parameters of such models and for the baseline hazard functions. The estimators of the regression coeffcients are shown asymptotically to follow a multivariate normal distribution with a sandwich-type covariance matrix that can be consistently estimated. The estimated baseline and subject-specific cumulative hazard processes are shown to converge weakly to a zero-mean Gaussian random field. The weak convergence properties for the corresponding survival processes are established. A resampling technique is proposed for constructing simultaneous confidence bands for the survival curve of a specific subject. The methodology is extended to a multivariate version of a class of partly parametric additive hazards model. Simulation studies are conducted to assess finite sample properties, and the method is illustrated with an application to development of coronary heart diseases and cardiovascular accidents in the Framingham Heart Study. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 801 818 http://hdl.handle.net/10.1093/biomet/91.4.801 text/html Access to full text is restricted to subscribers. Guosheng Yin Jianwen Cai

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:109-1212010-03-05RePEc:oup:biomet

article Phase I clinical studies are experiments in which a new drug is administered to humans to determine the maximum dose that causes toxicity with a target probability. Phase I dose-finding is often formulated as a quantile estimation problem. For studies with a biological endpoint, it is common to define toxicity by dichotomizing the continuous biomarker expression. In this article, we propose a novel variant of the Robbins--Monro stochastic approximation that utilizes the continuous measurements for quantile estimation. The Robbins--Monro method has seldom seen clinical applications, because it does not perform well for quantile estimation with binary data and it works with a continuum of doses that are generally not available in practice. To address these issues, we formulate the dose-finding problem as root-finding for the mean of a continuous variable, for which the stochastic approximation procedure is efficient. To accommodate the use of discrete doses, we introduce the idea of virtual observation that is defined on a continuous dosage range. Our proposed method inherits the convergence properties of the stochastic approximation algorithm and its computational simplicity. Simulations based on real trial data show that our proposed method improves accuracy compared with the continual re-assessment method and produces results robust to model misspecification. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 109 121 http://hdl.handle.net/10.1093/biomet/asp065 application/pdf Access to full text is restricted to subscribers. Ying Kuen Cheung Mitchell S. V. Elkind

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:15-302010-03-05RePEc:oup:biomet

article The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric and can have different covariance structures, for instance different smoothness parameters, in each component. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 15 30 http://hdl.handle.net/10.1093/biomet/asp078 application/pdf Access to full text is restricted to subscribers. Tatiyana V. Apanasovich Marc G. Genton

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:254-2592010-03-05RePEc:oup:biomet

article We study a discriminant direction vector that generally exists only in high-dimension, low sample size settings. Projections of data onto this direction vector take on only two distinct values, one for each class. There exist infinitely many such directions in the subspace generated by the data; but the maximal data piling vector has the longest distance between the projections. This paper investigates mathematical properties and classification performance of this discrimination method. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 254 259 http://hdl.handle.net/10.1093/biomet/asp084 application/pdf Access to full text is restricted to subscribers. Jeongyoun Ahn J. S. Marron

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:1-132010-03-05RePEc:oup:biomet

article Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on the variance of estimators in the case of one-dimensional systematic sampling. First we sketch a general approach to variance analysis using point process methods. We then analyze three different models for the error process, calculate exact expressions for the variances, and derive asymptotic variances. Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. This suggests that the current practice in some areas of microscopy may be based on over-optimistic predictions of estimator accuracy. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 1 13 http://hdl.handle.net/10.1093/biomet/asp067 application/pdf Access to full text is restricted to subscribers. Johanna Ziegel Adrian Baddeley Karl-Anton Dorph-Petersen Eva B. Vedel Jensen

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:223-2302010-03-05RePEc:oup:biomet

article We investigate tests for periodicity based on a spectral analysis of a time series, differentiating between global and local spectral-based tests. Global tests use information across the entire frequency band,whereas local tests are based on a window around the test frequency.We show that many spectral-based tests can be expressed in terms of a regression-based F test, which allows for approximate size and power calculations. Since global tests are usually derived assuming white noise errors, we extend to the correlated noise case. We demonstrate via a Monte Carlo study that although the global test may have better size and power, local tests are easier to use, and are comparable or better in terms of the power to detect periodicities, especially for spectra with a large dynamic range. We apply this methodology to a nonbehavioural test of hearing. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 223 230 http://hdl.handle.net/10.1093/biomet/asp079 application/pdf Access to full text is restricted to subscribers. L. Wei P. F. Craigmile

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:159-1702010-03-05RePEc:oup:biomet

article Higher-order approximations to p-values can be obtained from the loglikelihood function and a reparameterization that can be viewed as a canonical parameter in an exponential family approximation to the model. This approach clarifies the connection between Skovgaard (1996) and Fraser et al. (1999a), and shows that the Skovgaard approximation can be obtained directly using the mean loglikelihood function. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 159 170 http://hdl.handle.net/10.1093/biomet/asq001 application/pdf Access to full text is restricted to subscribers. N. Reid D. A. S. Fraser

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:199-2082010-03-05RePEc:oup:biomet

article Self-exciting threshold autoregressive time series models have been used extensively, and the conditional mean obtained from these models can be used to predict the future value of a random variable. In this paper we consider quantile forecasts of a time series based on the quantile self-exciting threshold autoregressive time series models proposed by Cai and Stander (2008) and present a new forecasting method for them. Simulation studies and application to real time series show that the method works very well. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 199 208 http://hdl.handle.net/10.1093/biomet/asp070 application/pdf Access to full text is restricted to subscribers. Yuzhi Cai

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:209-2142010-03-05RePEc:oup:biomet

article A simple case of Poisson regression is used to study the potential gain in efficiency from using a mixed model representation. Possible systematic errors arising from misspecification of the random terms in the model are examined. It is shown in particular that for a special but realistic problem, appreciable bias may arise from misspecification of a random component. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 209 214 http://hdl.handle.net/10.1093/biomet/asp083 application/pdf Access to full text is restricted to subscribers. D. R. Cox M. Y. Wong

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:238-2452010-03-05RePEc:oup:biomet

article A powerful technique for inference concerning spatial dependence in a random field is to use spectral methods based on frequency domain analysis. Here we develop a nonparametric Bayesian approach to statistical inference for the spectral density of a random field. We construct a multi-dimensional Bernstein polynomial prior for the spectral density and devise a Markov chain Monte Carlo algorithm to simulate from the posterior of the spectral density. The posterior sampling enables us to obtain a smoothed estimate of the spectral density as well as credible bands at desired levels. Simulation shows that our proposed method is more robust than a parametric approach. For illustration, we analyse a soil data example. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 238 245 http://hdl.handle.net/10.1093/biomet/asp066 application/pdf Access to full text is restricted to subscribers. Yanbing Zheng Jun Zhu Anindya Roy

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:123-1322010-03-05RePEc:oup:biomet

article Evaluating the causal effect of an exposure on a response from case-control and cohort studies is a major concern in epidemiological and medical research. Since causal effects are in general nonidentifiable from such studies, this paper derives bounds on two causal measures: the causal risk difference and the causal risk ratio. We use the potential response approach and a linear programming method to derive sharp bounds on the causal risk difference, and a novel fractional programming method to derive bounds on the causal risk ratio. In addition, in the presence of missing data, we consider three different missingness mechanisms and propose sharp bounds under these situations. The results provide new guidance on causal inference in case-control and cohort studies. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 123 132 http://hdl.handle.net/10.1093/biomet/asp076 application/pdf Access to full text is restricted to subscribers. Manabu Kuroki Zhihong Cai Zhi Geng

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:181-1982010-03-05RePEc:oup:biomet

article We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) for recovering an unknown high-dimensional Gaussian mean vector. The existing results for its upper error bounds over various sparse l_p-balls are extended to more general cases. We show that, for a properly chosen prior on the number of nonzero entries of the mean vector, the corresponding adaptive estimator is asymptotically minimax in a wide range of sparse and dense l_p-balls. The proposed procedure is then applied in a wavelet context to derive adaptive global and level-wise wavelet estimators of the unknown response function in the Gaussian white noise model. These estimators are then proven to be, respectively, asymptotically near-minimax and minimax in a wide range of Besov balls. These results are also extended to the estimation of derivatives of the response function. Simulated examples are conducted to illustrate the performance of the proposed level-wise wavelet estimator in finite sample situations, and to compare it with several existing counterparts. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 181 198 http://hdl.handle.net/10.1093/biomet/asp080 application/pdf Access to full text is restricted to subscribers. Felix Abramovich Vadim Grinshtein Athanasia Petsa Theofanis Sapatinas

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:65-782010-03-05RePEc:oup:biomet

article We consider solutions to generalized estimating equations with singular working correlation matrices, of which the estimator of Diggle et al. (2007) is a special case. We give explicit conditions for consistent estimation when the pattern of observations may be informative. In such cases, simulations reveal reduced bias and reduced mean squared error compared with existing alternatives. A study of peritoneal dialysis is used to illustrate the methodology. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 65 78 http://hdl.handle.net/10.1093/biomet/asp068 application/pdf Access to full text is restricted to subscribers. D. M. Farewell

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:171-1802010-03-05RePEc:oup:biomet

article We consider the doubly robust estimation of the parameters in a semiparametric conditional odds ratio model. Our estimators are consistent and asymptotically normal in a union model that assumes either of two variation independent baseline functions is correctly modelled but not necessarily both. Furthermore, when either outcome has finite support, our estimators are semiparametric efficient in the union model at the intersection submodel where both nuisance functions models are correct. For general outcomes, we obtain doubly robust estimators that are nearly efficient at the intersection submodel. Our methods are easy to implement as they do not require the use of the alternating conditional expectations algorithm of Chen (2007). Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 171 180 http://hdl.handle.net/10.1093/biomet/asp062 application/pdf Access to full text is restricted to subscribers. Eric J. Tchetgen Tchetgen James M. Robins Andrea Rotnitzky

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:147-1582010-03-05RePEc:oup:biomet

article We propose a new approach for analyzing skewed and heteroscedastic health care cost data through regression of the conditional quantiles of the transformed cost. Using the appealing equivariance property of quantiles to monotone transformations, we propose a distribution-free estimator of the conditional mean cost on the original scale. The proposed method is extended to a two-part heteroscedastic model to account for zero costs commonly seen in health care cost studies. Simulation studies indicate that the proposed estimator has competitive and more robust performance than existing estimators in various heteroscedastic models. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 147 158 http://hdl.handle.net/10.1093/biomet/asp072 application/pdf Access to full text is restricted to subscribers. Huixia Judy Wang Xiao-Hua Zhou

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:246-2532010-03-05RePEc:oup:biomet

article Outlier sums were proposed by Tibshirani & Hastie (2007) and Wu (2007) for detecting outlier genes where only a small subset of disease samples shows unusually high gene expression, but they did not develop their distributional properties and formal statistical inference. In this study, a new outlier sum for detection of outlier genes is proposed, its asymptotic distribution theory is developed, and the p-value based on this outlier sum is formulated. Its analytic form is derived on the basis of the large-sample theory. We compare the proposed method with existing outlier sum methods by power comparisons. Our method is applied to DNA microarray data from samples of primary breast tumors examined by Huang et al. (2003). The results show that the proposed method is more efficient in detecting outlier genes. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 246 253 http://hdl.handle.net/10.1093/biomet/asp075 application/pdf Access to full text is restricted to subscribers. Lin-An Chen Dung-Tsa Chen Wenyaw Chan

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:95-1082010-03-05RePEc:oup:biomet

article We introduce the use of stochastic ordering for defining treatment-related trend in clustered exchangeable binary data for both when cluster sizes are fixed and when they vary randomly. In the latter case, there is a well-documented tendency for such data to be sparse, a problem we address by making an assumption of interpretability or, equivalently, marginal compatibility. Our procedures are based on a representation of the joint distribution of binary exchangeable random variables by a saturated model, and may hence be considered nonparametric. The definition of trend by stochastic ordering is proposed to ensure a flexibility that allows for various forms of monotone increases in response to the cluster as a whole to be included in the evaluation of the trend. We obtain maximum likelihood estimates of probability functions under stochastic ordering using mixture-likelihood-based algorithms. Since the data are sparse, we avoid the use of asymptotic results and obtain p-values of the likelihood ratio procedures by permutation resampling. We demonstrate how the proposed framework can be used in risk assessment, and provide comparisons with existing procedures. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 95 108 http://hdl.handle.net/10.1093/biomet/asp077 application/pdf Access to full text is restricted to subscribers. Aniko Szabo E. Olusegun George

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:31-482010-03-05RePEc:oup:biomet

article In standard parametric classifiers, or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities, the prior probabilities of the respective populations play a key role. However, those probabilities are largely ignored in the construction of high-dimensional classifiers, partly because there are no likelihoods to be constructed or Bayes risks to be estimated. Nevertheless, including information about prior probabilities can reduce the overall error rate, particularly in cases where doing so is most important, i.e. when the classification problem is particularly challenging and error rates are not close to zero. In this paper we suggest a general approach to reducing error rate in this way, by using a method derived from Breiman's bagging idea. The potential improvements in performance are identified in theoretical and numerical work, the latter involving both applications to real data and simulations. The method is simple and explicit to apply, and does not involve choice of any tuning parameters. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 31 48 http://hdl.handle.net/10.1093/biomet/asp081 application/pdf Access to full text is restricted to subscribers. Peter Hall Jing-Hao Xue

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:133-1452010-03-05RePEc:oup:biomet

article We propose a semiparametric random effects model for multivariate competing risks data when the failures of a particular type are of interest. Under this model, the marginal cumulative incidence functions follow a generalized semiparametric additive model. The associations between the cause-specific failure times can be studied through dependence parameters of copula functions that are allowed to depend on cluster-level covariates. A cross-odds ratio-type measure is proposed to describe the associations between cause-specific failure times, and its relationship to the dependence parameters is explored. We develop a two-stage estimation procedure where the marginal models are estimated in the first stage and the dependence parameters are estimated in the second stage. The large sample properties of the proposed estimators are derived. The proposed procedures are applied to Danish twin data to model the cumulative incidence for the age of natural menopause and to investigate the association in the onset of natural menopause between monozygotic and dizygotic twins. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 133 145 http://hdl.handle.net/10.1093/biomet/asp082 application/pdf Access to full text is restricted to subscribers. Thomas H. Scheike Yanqing Sun Mei-Jie Zhang Tina Kold Jensen

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:49-642010-03-05RePEc:oup:biomet

article We extend the common linear functional regression model to the case where the dependency of a scalar response on a functional predictor is of polynomial rather than linear nature. Focusing on the quadratic case, we demonstrate the usefulness of the polynomial functional regression model, which encompasses linear functional regression as a special case. Our approach works under mild conditions for the case of densely spaced observations and also can be extended to the important practical situation where the functional predictors are derived from sparse and irregular measurements, as is the case in many longitudinal studies. A key observation is the equivalence of the functional polynomial model with a regression model that is a polynomial of the same order in the functional principal component scores of the predictor processes. Theoretical analysis as well as practical implementations are based on this equivalence and on basis representations of predictor processes. We also obtain an explicit representation of the regression surface that defines quadratic functional regression and provide functional asymptotic results for an increasing number of model components as the number of subjects in the study increases. The improvements that can be gained by adopting quadratic as compared to linear functional regression are illustrated with a case study that includes absorption spectra as functional predictors. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 49 64 http://hdl.handle.net/10.1093/biomet/asp069 application/pdf Access to full text is restricted to subscribers. Fang Yao Hans-Georg Müller

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:215-2222010-03-05RePEc:oup:biomet

article We propose pseudo-score confidence intervals for parameters in models for discrete data. The confidence interval is obtained by inverting a test that uses a Pearson chi-squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values. For multinomial models, the pseudo-score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test-based inferences. For cases in which ordinary score methods are impractical, such as when the likelihood function is not an explicit function of model parameters, the pseudo-score method is feasible. We illustrate the method for four such examples. Generalizations of the method are also presented for future research, including inference for complex sampling designs using a quasilikelihood Pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 215 222 http://hdl.handle.net/10.1093/biomet/asp074 application/pdf Access to full text is restricted to subscribers. Alan Agresti Euijung Ryu

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:79-932010-03-05RePEc:oup:biomet

article Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood-based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks theorem for the limiting distributions of the empirical likelihood ratios is derived. It is shown that one of the proposed methods is locally efficient among a class of within-subject variance-covariance matrices. A simulation study is conducted to investigate the finite sample properties of the proposed methods and compares them with the block empirical likelihood method by You et al. (2006) and the normal approximation with a correctly estimated variance-covariance. The results suggest that the proposed methods are generally more efficient than existing methods that ignore the correlation structure, and are better in coverage compared to the normal approximation with correctly specified within-subject correlation. An application illustrating our methods and supporting the simulation study results is presented. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 79 93 http://hdl.handle.net/10.1093/biomet/asp073 application/pdf Access to full text is restricted to subscribers. Suojin Wang Lianfen Qian Raymond J. Carroll

oai:RePEc:oup:biomet:v:97:y:2010:i:1:p:231-2372010-03-05RePEc:oup:biomet

article We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk-super-2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and nonstationary processes. Furthermore, at the unit root, the limiting distribution of the weighted least squares approximate restricted likelihood estimator is shown to be the zero-intercept Dickey--Fuller distribution, unlike the ordinary least squares with intercept estimator that has a different distribution with significantly higher bias. Copyright 2010, Oxford University Press. 1 2010 97 Biometrika 231 237 http://hdl.handle.net/10.1093/biomet/asp071 application/pdf Access to full text is restricted to subscribers. Willa W. Chen Rohit S. Deo

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:93-1062009-04-18RePEc:oup:biomet

article A critical issue in modelling binary response data is the choice of the links. We introduce a new link based on the generalized t-distribution. There are two parameters in the generalized t-link: one parameter purely controls the heaviness of the tails of the link and the second parameter controls the scale of the link. Two major advantages are offered by the generalized t-links. First, a symmetric generalized t-link with an unknown shape parameter is much more identifiable than a Student t-link with unknown degrees of freedom and a known scale parameter. Secondly, skewed generalized t-links with both unknown shape and scale parameters provide much more flexible and improved skewed link regression models than the existing skewed links. Various theoretical properties and attractive features of the proposed links are examined and explored in detail. An efficient Markov chain Monte Carlo algorithm is developed for sampling from the posterior distribution. The deviance information criterion measure is used for guiding the choice of links. The proposed methodology is motivated and illustrated by prostate cancer data. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 93 106 http://hdl.handle.net/10.1093/biomet/asm079 application/pdf Access to full text is restricted to subscribers. Sungduk Kim Ming-Hui Chen Dipak K. Dey

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:559-5782009-04-18RePEc:oup:biomet

article To compensate for item nonresponse, hot deck imputation procedures replace missing values with values that occur in the sample. Fractional hot deck imputation replaces each missing observation with a set of imputed values and assigns a weight to each imputed value. Under the model in which observations in an imputation cell are independently and identically distributed, fractional hot deck imputation is shown to be an effective imputation procedure. A consistent replication variance estimation procedure for estimators computed with fractional imputation is suggested. Simulations show that fractional imputation and the suggested variance estimator are superior to multiple imputation estimators in general, and much superior to multiple imputation for estimating the variance of a domain mean. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 559 578 Jae Kwang Kim

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:19-352009-04-18RePEc:oup:biomet

article We propose penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model. The methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite, and thus conduct model selection and estimation simultaneously. The implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix, but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization. We propose a <sc>BIC</sc>-type criterion for the selection of the tuning parameter in the penalized likelihood methods. The connection between our methods and existing methods is illustrated. Simulations and real examples demonstrate the competitive performance of the new methods. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 19 35 http://hdl.handle.net/10.1093/biomet/asm018 application/pdf Access to full text is restricted to subscribers. Ming Yuan Yi Lin

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:75-922009-04-18RePEc:oup:biomet

article Under a general regression setting, we propose an optimal unconditional prediction procedure for future responses. The resulting prediction intervals or regions have a desirable average coverage level over a set of covariate vectors of interest. When the working model is not correctly specified, the traditional conditional prediction method is generally invalid. On the other hand, one can empirically calibrate the above unconditional procedure and also obtain its crossvalidated counterpart. Various large and small sample properties of these unconditional methods are examined analytically and numerically. We find that the &Kscr;-fold crossvalidated procedure performs exceptionally well even for cases with rather small sample sizes. The new proposals are illustrated with two real examples, one with a continuous response and the other with a binary outcome. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 75 92 http://hdl.handle.net/10.1093/biomet/asm078 application/pdf Access to full text is restricted to subscribers. Tianxi Cai Lu Tian Scott D. Solomon L.J. Wei

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:209-2222009-04-18RePEc:oup:biomet

article We propose a Lagrange multiplier test for additivity based on the Bürmann expansion of a conditional mean function. The asymptotic null distribution of the test is shown to be x-super-2, under some regularity conditions. In contrast, the Lagrange multiplier test proposed by Chen et al. (1995) is based on the Volterra expansion of the conditional mean function. We discuss some desirable advantages of the Bürmann expansion over the Volterra expansion for nonlinear time series modelling. We also reported an empirical study which shows that, in terms of empirical power, the Lagrange multiplier test motivated by the Bürmann expansion outperforms the test of Chen et al. (1995) for the cases for which the Lagrange multiplier test is designed. For other cases for which none of the tests is specifically designed, the empirical powers of the two tests are comparable. Finally, we illustrated the use of the Lagrange multiplier test with a blowfly experimental system. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 209 222 K. S. Chan

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:863-8762009-04-18RePEc:oup:biomet

article A well-known and useful method for generalised regression analysis when a linear covariate x is available only through some approximation z is to carry out more or less the usual analysis with E(x|z) substituted for x. Sometimes, but not always, the quantity var (x|z) should be used to allow for overdispersion introduced by this substitution. These quantities involve the distribution of true covariates x, and with some exceptions this requires assessment of that distribution through the distribution of observed values z. It is often desirable to take a nonparametric approach to this, which inherently involves a deconvolution that is difficult to carry our directly. However, if covariate errors are assumed to be multiplicative and log-normal, simple but accurate approximations are available for the quantities E(x-super-k|z) (k &equals; 1, 2, …). In particular, the approximations depend only on the first two derivatives of the logarithm of the density of z at the point under consideration and the coefficient of variation of z|x. The methods will thus be most useful in large-scale observational studies where the distribution of z can be assessed well enough in an essentially nonparametric manner to approximate adequately those derivatives. We consider both the classical and Berkson error models. This approach is applied to radiation dose estimates for atomic-bomb survivors. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 863 876 http://hdl.handle.net/10.1093/biomet/91.4.863 text/html Access to full text is restricted to subscribers. Donald A. Pierce Albrecht M. Kellerer

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:979-9862009-04-18RePEc:oup:biomet

article We consider the identification problem that arises in the age-period-cohort models as well as in the extended chain-ladder model. We propose a canonical parameterization based on the accelerations of the trends in the three factors. This parameterization is exactly identified and eases interpretation, estimation and forecasting. The canonical parameterization is applied to a class of index sets which have trapezoidal shapes, including various Lexis diagrams and the insurance-reserving triangles. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 979 986 http://hdl.handle.net/10.1093/biomet/asn026 application/pdf Access to full text is restricted to subscribers. D. Kuang B. Nielsen J. P. Nielsen

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:107-1222009-04-18RePEc:oup:biomet

article We develop a unified L₁-based analysis-of-variance-type method for testing linear hypotheses. Like the classical L₂-based analysis of variance, the method is coordinate-free in the sense that it is invariant under any linear transformation of the covariates or regression parameters. Moreover, it allows singular design matrices and heterogeneous error terms. A simple approximation using stochastic perturbation is proposed to obtain cut-off values for the resulting test statistics. Both test statistics and distributional approximations can be computed using standard linear programming. An asymptotic theory is derived for the method. Special cases of one- and multi-way analysis of variance and analysis of covariance models are worked out in detail. The main results of this paper can be extended to general quantile regression. Extensive simulations show that the method works well in practical settings. The method is also applied to a dataset from General Social Surveys. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 107 122 http://hdl.handle.net/10.1093/biomet/asm082 application/pdf Access to full text is restricted to subscribers. Kani Chen Zhiliang Ying Hong Zhang Lincheng Zhao

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:375-3882009-04-18RePEc:oup:biomet

article Dealing with missing data via parametric multiple imputation methods usually implies stating several strong assumptions both about the distribution of the data and about underlying regression relationships. If such parametric assumptions do not hold, the multiply imputed data are not appropriate and might produce inconsistent estimators and thus misleading results. In this paper, a fully nonparametric and a semiparametric imputation method are studied, both based on local resampling principles. It is shown that the final estimator, based on these local imputations, is consistent under fewer or no parametric assumptions. Asymptotic expressions for bias, variance and mean squared error are derived, showing the theoretical impact of the different smoothing parameters. Simulations illustrate the usefulness and applicability of the method. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 375 388 Marc Aerts

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:961-9772009-04-18RePEc:oup:biomet

article Testing of multiple hypotheses involves statistics that are strongly dependent in some applications, but most work on this subject is based on the assumption of independence. We propose a new method for estimating the false discovery rate of multiple hypothesis tests, in which the density of test scores is estimated parametrically by minimizing the Kullback--Leibler distance between the unknown density and its estimator using the stochastic approximation algorithm, and the false discovery rate is estimated using the ensemble averaging method. Our method is applicable under general dependence between test statistics. Numerical comparisons between our method and several competitors, conducted on simulated and real data examples, show that our method achieves more accurate control of the false discovery rate in almost all scenarios. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 961 977 http://hdl.handle.net/10.1093/biomet/asn036 application/pdf Access to full text is restricted to subscribers. Faming Liang Jian Zhang

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:49-602009-04-18RePEc:oup:biomet

article We extend the optimal symmetric group sequential tests of Eales & Jennison (1992) to the broader class of asymmetric designs. Two forms of asymmetry are considered, involving unequal type I and type II error rates and different emphases on expected sample sizes at the null and alternative hypotheses. We discuss the properties of our optimal designs and use them to assess the efficiency of the family of tests proposed by Pampallona & Tsiatis (1994) and two families of one-sided tests defined through error spending functions. We show that the error spending designs are highly efficient, while the easily implemented tests of Pampallona & Tsiatis are a little less efficient but still not far from optimal. Our results demonstrate that asymmetric designs can decrease the expected sample size under one hypothesis, but only at the expense of a significantly larger expected sample size under the other hypothesis. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 49 60 Stuart Barber

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:893-9122009-04-18RePEc:oup:biomet

article A balanced sampling design is defined by the property that the Horvitz--Thompson estimators of the population totals of a set of auxiliary variables equal the known totals of these variables. Therefore the variances of estimators of totals of all the variables of interest are reduced, depending on the correlations of these variables with the controlled variables. In this paper, we develop a general method, called the cube method, for selecting approximately balanced samples with equal or unequal inclusion probabilities and any number of auxiliary variables. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 893 912 http://hdl.handle.net/10.1093/biomet/91.4.893 text/html Access to full text is restricted to subscribers. Jean-Claude Deville Yves Tille

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:765-7752009-04-18RePEc:oup:biomet

article Random effects logistic regression models are often used to model clustered binary response data. Regression parameters in these models have a conditional, subject-specific interpretation in that they quantify regression effects for each cluster. Very often, the logistic functional shape conditional on the random effects does not carry over to the marginal scale. Thus, parameters in these models usually do not have an explicit marginal, population-averaged interpretation. We study a bridge distribution function for the random effect in the random intercept logistic regression model. Under this distributional assumption, the marginal functional shape is still of logistic form, and thus regression parameters have an explicit marginal interpretation. The main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework. The generality of the results and some properties of the bridge distribution functions are discussed. An example is used for illustration. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 765 775 Zengri Wang

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:233-2402009-04-18RePEc:oup:biomet

article We propose an alternative representation of the cause-specific cross hazard ratio for bivariate competing risks data. The representation leads to a simple plug-in estimator, unlike an existing ad hoc procedure. The large sample properties of the resulting inferences are established. Simulations and a real data example demonstrate that the proposed methodology may substantially reduce the computational burden of the existing procedure, while maintaining similar efficiency properties. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 233 240 http://hdl.handle.net/10.1093/biomet/asm089 application/pdf Access to full text is restricted to subscribers. Yu Cheng Jason P. Fine

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:85-972009-04-18RePEc:oup:biomet

article Two moment-based model-fitting procedures for the heteroscedastic factor analysis model are introduced and compared. The procedures produce consistent parameter estimators and asymptotically valid inferences for heteroscedasticity without specifying the distributional forms for the factor and heteroscedastic errors. Also, an individual-specific inference procedure for the factor score is developed. Simulation studies show the practical usefulness of the procedures. An example from a morphological measurement study is described. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 85 97 Sock-Cheng Lewin-Koh

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:529-5422009-04-18RePEc:oup:biomet

article We consider parametric frameworks for the prediction of future values of a random variable Y, based on previously observed data X. Simple pivotal methods for obtaining calibrated prediction intervals are presented and illustrated. Frequentist predictive distributions are defined as confidence distributions, and their utility is demonstrated. A simple pivotal-based approach that produces prediction intervals and predictive distributions with well-calibrated frequentist probability interpretations is introduced, and efficient simulation methods for producing predictive distributions are considered. Properties related to an average Kullback--Leibler measure of goodness for predictive or estimated distributions are given. The predictive distributions here are shown to be optimal in certain settings with invariance structure, and to dominate plug-in distributions under certain conditions. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 529 542 http://hdl.handle.net/10.1093/biomet/92.3.529 text/html Access to full text is restricted to subscribers. J. F. Lawless Marc Fredette

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:927-9412009-04-18RePEc:oup:biomet

article When used for modelling longitudinal data generalised estimating equations specify a working structure for the within-subject covariance matrices, aiming to produce efficient parameter estimators. However, misspecification of the working covariance structure may lead to a large loss of efficiency of the estimators of the mean parameters. In this paper we propose an approach for joint modelling of the mean and covariance structures of longitudinal data within the framework of generalised estimating equations. The resulting estimators for the mean and covariance parameters are shown to be consistent and asymptotically Normally distributed. Real data analysis and simulation studies show that the proposed approach yields e?cient estimators for both the mean and covariance parameters. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 927 941 http://hdl.handle.net/10.1093/biomet/93.4.927 text/html Access to full text is restricted to subscribers. Huajun Ye Jianxin Pan

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:861-8762009-04-18RePEc:oup:biomet

article For the problem of dual system estimation, we propose a Bayesian treed capture-recapture model to account for heterogeneity of capture probabilities where individual auxiliary information is available. The model uses a binary tree to partition the covariate space into 'homogeneous' regions, within each of which the capture response can be described adequately by a simple model that assumes equal catchability. The attractive features of the proposed model include reduction of correlation bias, robustness and practical flexibility as well as simplicity and interpretability. In addition, it provides a systematic and effective way of forming post-strata for the Sekar--Deming estimator of population size. We compare the performance of estimators based on this model to those of alternative estimators in three scenarios. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 861 876 http://hdl.handle.net/10.1093/biomet/93.4.861 text/html Access to full text is restricted to subscribers. Xinlei Wang Johan Lim S. Lynne Stokes

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:217-2292009-04-18RePEc:oup:biomet

article We consider variable selection in the single-index model. We prove that the popular leave-m-out crossvalidation method has different behaviour in the single-index model from that in linear regression models or nonparametric regression models. A new consistent variable selection method, called separated crossvalidation, is proposed. Further analysis suggests that the method has better finite-sample performance and is computationally easier than leave-m-out crossvalidation. Separated crossvalidation, applied to the Swiss banknotes data and the ozone concentration data, leads to single-index models with selected variables that have better prediction capability than models based on all the covariates. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 217 229 http://hdl.handle.net/10.1093/biomet/asm008 application/pdf Access to full text is restricted to subscribers. Efang Kong Yingcun Xia

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:411-4212009-04-18RePEc:oup:biomet

article A goodness-of-fit test statistic for spatial point processes is proposed and shown to have an asymptotic chi-squared distribution if the underlying point process is Poisson. Simulations demonstrate that the test, when testing for complete spatial randomness, is more sensitive to mixtures of regular and clustered point processes than the tests using the nearest neighbour distance distribution, the second- or third-order characteristics. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 411 421 P. Grabarnik

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:234-2412009-04-18RePEc:oup:biomet

article Beran & Hall's (1993) simple linear interpolation provides a very convenient approach for constructing nonparametric confidence intervals for population quantiles based on a random sample of size n. We show that the coverage error of the interpolated interval, which is of order O(n-super- - 1), can be improved upon by calibrating the nominal coverage level. Three distinct methods of calibration are considered. The analytical and Monte Carlo methods succeed in reducing the order of coverage error to O(n-super- - 3/2), while the smoothed bootstrap method reduces it further to O(n-super- - 25/14).We provide guidelines for practical implementation of the calibration methods. Their performance is compared with the simple linear interpolated interval in a simulation study which confirms superiority of the calibrated intervals. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 234 241 http://hdl.handle.net/10.1093/biomet/92.1.234 text/html Access to full text is restricted to subscribers. Yvonne H. S. Ho Stephen M. S. Lee

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:921-9362009-04-18RePEc:oup:biomet

article Two asymptotic frameworks, increasing domain asymptotics and infill asymptotics, have been advanced for obtaining limiting distributions of maximum likelihood estimators of covariance parameters in Gaussian spatial models with or without a nugget effect. These limiting distributions are known to be different in some cases. It is therefore of interest to know, for a given finite sample, which framework is more appropriate. We consider the possibility of making this choice on the basis of how well the limiting distributions obtained under each framework approximate their finite-sample counterparts. We investigate the quality of these approximations both theoretically and empirically, showing that, for certain consistently estimable parameters of exponential covariograms, approximations corresponding to the two frameworks perform about equally well. For those parameters that cannot be estimated consistently, however, the infill asymptotic approximation is preferable. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 921 936 http://hdl.handle.net/10.1093/biomet/92.4.921 text/html Access to full text is restricted to subscribers. Hao Zhang Dale L. Zimmerman

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:787-7992009-04-18RePEc:oup:biomet

article Typical alternative hypotheses in the analysis of residuals of a standard regression model are considered, and for each one a Bayesian diagnostic based on a symmetric form of the Kullback--Leibler divergence is determined. The results include an explicit expression for the diagnostic when the alternative hypothesis is that the errors are generated by an unknown distribution function with a Dirichlet process prior. This expression is immediately interpretable, exactly computable and endowed with important asymptotic connections. A linear approximation of the diagnostic reveals close links with the class of Lagrange multiplier test statistics. When the alternative hypothesis is that the errors are generated by an autoregressive process the linear approximation is proportional to the Box--Pierce statistic or to the Ljung--Box statistic, according to the characteristics of the prior, if the observations have zero mean; it depends on the Durbin--Watson statistic if the errors are first-order autoregressive, and it is related to the Cliff--Ord statistic if they are generated by a first-order spatial autoregression. The sensitivity to the prior of the diagnostic and of its linear approximation is also discussed. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 787 799 http://hdl.handle.net/10.1093/biomet/92.4.787 text/html Access to full text is restricted to subscribers. Cinzia Carota

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:759-7712009-04-18RePEc:oup:biomet

article The ordinary Bayesian information criterion is too liberal for model selection when the model space is large. In this paper, we re-examine the Bayesian paradigm for model selection and propose an extended family of Bayesian information criteria, which take into account both the number of unknown parameters and the complexity of the model space. Their consistency is established, in particular allowing the number of covariates to increase to infinity with the sample size. Their performance in various situations is evaluated by simulation studies. It is demonstrated that the extended Bayesian information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate, a desirable property in many applications. The extended Bayesian information criteria are extremely useful for variable selection in problems with a moderate sample size but with a huge number of covariates, especially in genome-wide association studies, which are now an active area in genetics research. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 759 771 http://hdl.handle.net/10.1093/biomet/asn034 application/pdf Access to full text is restricted to subscribers. Jiahua Chen Zehua Chen

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:481-4882009-04-18RePEc:oup:biomet

article The propensity score collapses the covariates of an observational study into a single measure summarizing their joint association with treatment conditions; prognostic scores summarize covariates' association with potential responses. As with propensity scores, stratification on prognostic scores brings to uncontrolled studies a concrete and desirable form of balance, a balance that is more familiar as an objective of experimental control. Like propensity scores, prognostic scores can reduce the dimension of the covariate, yet causal inferences conditional on them are as valid as are inferences conditional only on the unreduced covariate. As a method of adjustment unto itself, prognostic scoring has limitations not shared with propensity scoring, but it holds promise as a complement to the propensity score, particularly in certain designs for which unassisted propensity adjustment is difficult or infeasible. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 481 488 http://hdl.handle.net/10.1093/biomet/asn004 application/pdf Access to full text is restricted to subscribers. Ben B. Hansen

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:197-2102009-04-18RePEc:oup:biomet

article <?Pub Caret> We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the proposed estimators via shrinking asymptotics, assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound. With this type of asymptotic model we can uniquely determine the spectral density, avoiding the aliasing problem. We also present a new class of nonstationary processes, based on a convolution of local stationary processes. This model has the advantage that the model is simultaneously defined everywhere, unlike 'moving window' approaches, but it retains the attractive property that, locally in small regions, it behaves like a stationary spatial process. Applications include the spatial analysis and modelling of air pollution data provided by the US Environmental Protection Agency. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 197 210 Montserrat Fuentes

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:847-8622009-04-18RePEc:oup:biomet

article For bivariate current status data with univariate monitoring times, the identifiable part of the joint distribution is three univariate cumulative distribution functions, namely the two marginal distributions and the bivariate cumulative distribution function evaluated on the diagonal. We show that smooth functionals of these univariate cumulative distribution functions can be efficiently estimated with easily computed nonparametric maximum likelihood estimators based on reduced data consisting of univariate current status observations. This theory is then applied to functionals that address independence of the two survival times and the goodness-of-fit of a copula model used by Wang & Ding (2000). Some brief simulations are provided along with an illustration based on data on HIV transmission. Extension of the ideas to incorporate covariates, possibly time-dependent, are discussed. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 847 862 http://hdl.handle.net/10.1093/biomet/92.4.847 text/html Access to full text is restricted to subscribers. Nicholas P. Jewell Mark van der Laan Xiudong Lei

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:1003-10102009-04-18RePEc:oup:biomet

article We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimators of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-squared distribution under the null hypothesis that the mixing distribution is correctly specified. This strategy uses an idea presented by Hausman (1978), who considered analogous tests for the linear mixed model. An important advantage of the methods outlined here is that the resulting diagnostic test is easily implemented in commercial software. We illustrate the method by applying it to data from a clinical trial investigating the effect of hormonal contraceptives in women. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 1003 1010 http://hdl.handle.net/10.1093/biomet/93.4.1003 text/html Access to full text is restricted to subscribers. Eric J. Tchetgen Brent A. Coull

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:645-6592009-04-18RePEc:oup:biomet

article We consider the estimation of parameters of a multiple regression model with nonstationary errors. We assume the nonstationary errors satisfy a time-dependent autoregressive process and describe a method for estimating the parameters of the regressors and the time-dependent autoregressive parameters. The parameters are rescaled as in nonparametric regression to obtain the asymptotic sampling properties of the estimators. The method is illustrated with an example taken from global temperature anomalies. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 645 659 Suhasini Subba Rao

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:437-4492009-04-18RePEc:oup:biomet

article We investigate the effects of measurement error on the estimation of nonparametric variance functions. We show that either ignoring measurement error or direct application of the simulation extrapolation, SIMEX, method leads to inconsistent estimators. Nevertheless, the direct SIMEX method can reduce bias relative to a naive estimator. We further propose a permutation SIMEX method that leads to consistent estimators in theory. The performance of both the SIMEX methods depends on approximations to the exact extrapolants. Simulations show that both the SIMEX methods perform better than ignoring measurement error. The methodology is illustrated using microarray data from colon cancer patients. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 437 449 http://hdl.handle.net/10.1093/biomet/asn017 application/pdf Access to full text is restricted to subscribers. Raymond J. Carroll Yuedong Wang

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:735-7442009-04-18RePEc:oup:biomet

article A conceptually simple quantile inference procedure is proposed for cause-specific failure probabilities with competing risks data. The quantiles are defined using the cumulative incidence function, which is intuitively meaningful in the competing–risks set–up. We establish the uniform consistency and weak convergence of a nonparametric estimator of this quantile function. These results form the theoretical basis for extensions of standard one–sample and two–sample quantile inference for independently censored data. This includes the construction of confidence intervals and bands for the quantile function, and two–sample tests. Simulation studies and a real data example illustrate the practical utility of the methodology. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 735 744 http://hdl.handle.net/10.1093/biomet/asm059 application/pdf Access to full text is restricted to subscribers. L. Peng J. P. Fine

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:234-2392009-04-18RePEc:oup:biomet

article In the Lancaster representation a joint density is decomposed into a sum of additive interactions. Using these interactions, we derive conditions for checking compatibility among a collection of marginal densities. The representation also shows how to construct an all-positive joint density additively from a given set of compatible marginals. An algorithm is proposed for reducing the dimension of the marginal densities so that compatibility can be checked in sequential increments. The representation may yield insights into the construction and simulation of models represented by undirected graphs. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 234 239 Yuchung J. Wang

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:123-1372009-04-18RePEc:oup:biomet

article We study nonparametric regression for correlated failure time data. Kernel estimating equations are used to estimate nonparametric covariate effects. Independent and weighted-kernel estimating equations are studied. The derivative of the nonparametric function is first estimated and the nonparametric function is then estimated by integrating the derivative estimator. We show that the nonparametric kernel estimator is consistent for any arbitrary working correlation matrix and that its asymptotic variance is minimized by assuming working independence. We evaluate the performance of the proposed kernel estimator using simulation studies, and apply the proposed method to the western Kenya parasitaemia data. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 123 137 http://hdl.handle.net/10.1093/biomet/asm081 application/pdf Access to full text is restricted to subscribers. Zhangsheng Yu Xihong Lin

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:15-272009-04-18RePEc:oup:biomet

article In multi-state models regression analysis typically involves the modelling of each transition intensity separately. Each probability of interest, namely the probability that a subject will be in a given state at some time, is a complex nonlinear function of the intensity regression coefficients. We present a technique which models the state probabilities directly. This method is based on the pseudo-values from a jackknife statistic constructed from simple summary statistic estimates of the state probabilities. These pseudo-values are then used in a generalised estimating equation to obtain estimates of the model parameters. We illustrate how this technique works by studying examples of common regression problems. We apply the technique to model acute graft-versus-host disease in bone marrow transplants. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 15 27 Per Kragh Andersen

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:747-7642009-04-18RePEc:oup:biomet

article We consider multivariate regression analysis with missing data in the outcome variables, when the nonresponse mechanism depends on the underlying values of the responses and hence is nonignorable. Related problems include response-biased sampling where data are sampled with probability depending only on the univariate response. Our methods do not require specification of the form of the nonresponse mechanism. We show that, under certain regularity conditions, all the regression parameters can be identified from a conditional likelihood based on the complete cases, if the marginal distribution of the covariates is known. If the marginal distribution of the covariates is estimated from the data, then the regression parameters are identified from a pseudolikelihood resulting from substituting the estimated marginal distribution of the covariates in the above conditional likelihood. Simulation studies suggest that the pseudolikelihood method is approximately unbiased. In order to identify the model parameters, usually the dimension of the covariates and observed responses is required to be at least as large as the dimension of the missing responses. The method can also be modified to handle partial information about the missing-data mechanism. We also consider the special case where the missing data have a monotone pattern, where better use of the incomplete information can be made under certain assumptions. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 747 764 Gong Tang

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:613-6272009-04-18RePEc:oup:biomet

article Data arising in certain radio-tracking experiments consist of both a continuous spatial component and a discrete component related to behaviour. This leads naturally to stochastic models with a state space which is a product of continuous and discrete components. We consider a class of such models in continuous time, which can be thought of as diffusions in random environments. They are related to switching diffusion or hidden Markov models, but observations are made on both components at discrete time points, so that neither component is completely 'hidden'. We describe and illustrate an approach to fully Bayesian inference for these general models. The algorithm used is a hybrid Markov chain Monte Carlo method. The diffusion parameters, the environment parameters and the sample path of the environment process itself are updated separately, in sequence, and the individual steps are a mixture of Gibbs and random walk Metropolis--Hastings types. Some implementation and model checking issues are discussed, and an example using data arising from a radio-tracking experiment is described. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 613 627 P. G. Blackwell

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:1-182009-04-18RePEc:oup:biomet

article A smooth Gaussian random field with zero mean and unit variance is sampled on a discrete lattice, and we are interested in the exceedance probability or P-value of the maximum in a finite region. If the random field is smooth relative to the mesh size, then the P-value can be well approximated by results for the continuously sampled smooth random field (Adler, 1981; Worsley, 1995a; Taylor & Adler, 2003; Adler & Taylor, 2007). If the random field is not smooth, so that adjacent lattice values are nearly independent, then the usual Bonferroni bound is very accurate. The purpose of this paper is to bridge the gap between the two, and derive a simple, accurate upper bound for intermediate mesh sizes. The result uses a new improved Bonferroni-type bound based on discrete local maxima. We give an application to the 'bubbles' technique for detecting areas of the face used to discriminate fear from happiness. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 1 18 http://hdl.handle.net/10.1093/biomet/asm004 application/pdf Access to full text is restricted to subscribers. J. E. Taylor K. J. Worsley F. Gosselin

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:17-332009-04-18RePEc:oup:biomet

article Undetected confounding may severely distort the effect of an explanatory variable on a response variable, as defined by a stepwise data-generating process. The best known type of distortion, which we call direct confounding, arises from an unobserved explanatory variable common to a response and its main explanatory variable of interest. It is relevant mainly for observational studies, since it is avoided by successful randomization. By contrast, indirect confounding, which we identify in this paper, is an issue also for intervention studies. For general stepwise-generating processes, we provide matrix and graphical criteria to decide which types of distortion may be present, when they are absent and how they are avoided. We then turn to linear systems without other types of distortion, but with indirect confounding. For such systems, the magnitude of distortion in a least-squares regression coefficient is derived and shown to be estimable, so that it becomes possible to recover the effect of the generating process from the distorted coefficient. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 17 33 http://hdl.handle.net/10.1093/biomet/asm092 application/pdf Access to full text is restricted to subscribers. Nanny Wermuth D. R. Cox

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:265-2782009-04-18RePEc:oup:biomet

article A frequently encountered challenge in high-dimensional regression is the detection of relevant variables. Variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated. When taking the multiplicity of the testing problem into account, the power diminishes even further. To gain power and insight, it can be advantageous to look for influence not at the level of individual variables but rather at the level of clusters of highly correlated variables. We propose a hierarchical approach. Variable importance is first tested at the coarsest level, corresponding to the global null hypothesis. The method then tries to attribute any effect to smaller subclusters or even individual variables. The smallest possible clusters, which still exhibit a significant influence on the response variable, are retained. It is shown that the proposed testing procedure controls the familywise error rate at a prespecified level, simultaneously over all resolution levels. The method has power comparable to the Bonferroni--Holm procedure on the level of individual variables and dramatically larger power for coarser resolution levels. The best resolution level is selected adaptively. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 265 278 http://hdl.handle.net/10.1093/biomet/asn007 application/pdf Access to full text is restricted to subscribers. Nicolai Meinshausen

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:242-2472009-04-18RePEc:oup:biomet

article We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new estimator performs well when its tuning parameter is selected by either the Bayesian information criterion or the residual information criterion. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 242 247 http://hdl.handle.net/10.1093/biomet/92.1.242 text/html Access to full text is restricted to subscribers. Liqiang Ni R. Dennis Cook Chih-Ling Tsai

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:313-3342009-04-18RePEc:oup:biomet

article We consider Bayesian inference via Markov chain Monte Carlo for a variety of fractal Gaussian processes on the real line. These models have unknown parameters in the covariance matrix, requiring inversion of a new covariance matrix at each Markov chain Monte Carlo iteration. The processes have no suitable independence properties so this becomes computationally prohibitive. We surmount these difficulties by developing a computational algorithm for likelihood evaluation based on a 'multiresolution approximation' to the original process. The method is computationally very efficient and widely applicable, making likelihood-based inference feasible for large datasets. A simulation study indicates that this approach leads to accurate estimates for underlying parameters in fractal models, including fractional Brownian motion and fractional Gaussian noise, and functional parameters in the recently introduced multifractional Brownian motion. We apply the method to a variety of real datasets and illustrate its application to prediction and to model selection. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 313 334 http://hdl.handle.net/10.1093/biomet/asm025 application/pdf Access to full text is restricted to subscribers. Kenneth Falconer Carmen Fernández

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:907-9172009-04-18RePEc:oup:biomet

article There have been studies on how the asymptotic efficiency of a nonparametric function estimator depends on the handling of the within-cluster correlation when nonparametric regression models are used on longitudinal or cluster data. In particular, methods based on smoothing splines and local polynomial kernels exhibit different behaviour. We show that the generalized estimation equations based on weighted least squares regression splines for the nonparametric function have an interesting property: the asymptotic bias of the estimator does not depend on the working correlation matrix, but the asymptotic variance, and therefore the mean squared error, is minimized when the true correlation structure is specified. This property of the asymptotic bias distinguishes regression splines from smoothing splines. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 907 917 http://hdl.handle.net/10.1093/biomet/asn041 application/pdf Access to full text is restricted to subscribers. Zhongyi Zhu Wing K. Fung Xuming He

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:465-4712009-04-18RePEc:oup:biomet

article We propose a parametric wavelet thresholding procedure for estimation in the 'function plus independent, identically distributed Gaussian noise' model. To reflect the decreasing sparsity of wavelet coefficients from finer to coarser scales, our thresholds also decrease. They retain the noise-free reconstruction property while being lower than the universal threshold, and are jointly parameterised by a single scalar parameter. We show that our estimator achieves near-optimal risk rates for the usual range of Besov spaces. We propose a crossvalidation technique for choosing the parameter of our procedure. A simulation study demonstrates very good performance of our estimator compared to other state-of-the-art techniques. We discuss an extension to non-Gaussian noise. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 465 471 http://hdl.handle.net/10.1093/biomet/93.2.465 text/html Access to full text is restricted to subscribers. Anestis Antoniadis Piotr Fryzlewicz

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:246-2482009-04-18RePEc:oup:biomet

article This note points out a problem in the multi-move sampler as proposed by Shephard & Pitt (1997) and provides an alternative correct formulation. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 246 248 Toshiaki Watanabe

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:255-2682009-04-18RePEc:oup:biomet

article Small area estimation techniques typically rely on regression models that use both covariates and random effects to explain variation between the areas. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier-robust inference. We describe a new approach to small area estimation that is based on modelling quantilelike parameters of the conditional distribution of the target variable given the covariates. This avoids the problems associated with specification of random effects, allowing inter-area differences to be characterised by area-specific M-quantile coefficients. The proposed approach is easily made robust against outlying data values and can be adapted for estimation of a wide range of area-specific parameters, including quantiles of the distribution of the target variable in the different small areas. The differences between M-quantile and random effects models are discussed and the alternative approaches to small area estimation are compared using both simulated and real data. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 255 268 http://hdl.handle.net/10.1093/biomet/93.2.255 text/html Access to full text is restricted to subscribers. Ray Chambers Nikos Tzavidis

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:75-892009-04-18RePEc:oup:biomet

article We introduce covariate-adjusted regression for situations where both predictors and response in a regression model are not directly observable, but are contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate. We demonstrate how the regression coefficients can be estimated by establishing a connection to varying-coefficient regression. The proposed covariate-adjustment method is illustrated with an analysis of the regression of plasma fibrinogen concentration as response on serum transferrin level as predictor for 69 haemodialysis patients. In this example, both response and predictor are thought to be influenced in a multiplicative fashion by body mass index. A bootstrap hypothesis test enables us to test the significance of the regression parameters. We establish consistency and convergence rates of the parameter estimators for this new covariate-adjusted regression model. Simulation studies demonstrate the efficacy of the proposed method. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 75 89 http://hdl.handle.net/10.1093/biomet/92.1.75 text/html Access to full text is restricted to subscribers. Damla Şenturk Hans-Georg Muller

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:491-5072009-04-18RePEc:oup:biomet

article The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null hypotheses are not true, the procedure is conservative by a factor which is the proportion m-sub-0/m of the true null hypotheses among the hypotheses. We provide a new two-stage procedure in which the linear step-up procedure is used in stage one to estimate m-sub-0, providing a new level q′ which is used in the linear step-up procedure in the second stage. We prove that a general form of the two-stage procedure controls the false discovery rate at the desired level q. This framework enables us to study analytically the properties of other procedures that exist in the literature. A simulation study is presented that shows that two-stage adaptive procedures improve in power over the original procedure, mainly because they provide tighter control of the false discovery rate. We further study the performance of the current suggestions, some variations of the procedures, and previous suggestions, in the case where the test statistics are positively dependent, a case for which the original procedure controls the false discovery rate. In the setting studied here the newly proposed two-stage procedure is the only one that controls the false discovery rate. The procedures are illustrated with two examples of biological importance. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 491 507 http://hdl.handle.net/10.1093/biomet/93.3.491 text/html Access to full text is restricted to subscribers. Yoav Benjamini Abba M. Krieger Daniel Yekutieli

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:271-2822009-04-18RePEc:oup:biomet

article To compare two samples of censored data, we propose a unified method of semi-parametric inference for the parameter of interest when the model for one sample is parametric and that for the other is nonparametric. The parameter of interest may represent, for example, a comparison of means, or survival probabilities. The confidence interval derived from the semiparametric inference, which is based on the empirical likelihood principle, improves its counterpart constructed from the common estimating equation. The empirical likelihood ratio is shown to be asymptotically chi-squared. Simulation experiments illustrate that the method based on the empirical likelihood substantially outperforms the method based on the estimating equation. A real dataset is analysed. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 271 282 http://hdl.handle.net/10.1093/biomet/92.2.271 text/html Access to full text is restricted to subscribers. Yong Zhou Hua Liang

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:807-8172009-04-18RePEc:oup:biomet

article The intrinsic heterogeneity of individuals is a potential source of bias in estimation procedures for capture-recapture models. To account for this heterogeneity in the model a hierarchical structure has been proposed whereby the probabilities that each animal is caught on a single occasion are modelled as independent draws from a common unknown distribution F. However, there is general agreement that modelling F by a simple parametric curve may lead to unsatisfactory results. Here we propose an alternative Bayesian approach that relies on a different parameterisation which imposes no assumption on the shape of F but drives the problem back to a finite-dimensional setting. Our approach avoids some identifiability issues related to such a recapture model while allowing for a formal Bayesian default analysis. Results of analyses of computer simulations and of real data show that the method performs well. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 807 817 Luca Tardella

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:551-5662009-04-18RePEc:oup:biomet

article We present a general class of nonlinear regression and time series models that we call generalised structured models. The class is a natural generalisation of generalised additive models, and it includes generalised interaction models, structured volatility models, visual GARCH, generalised autoregressive conditional heteroscedasticity, models and varying coefficient models. We discuss estimation principles including smoothing splines and a generalisation of the projection approach of Mammen et al. (1999). We finish the paper with some theoretical considerations about the asymptotic performance of the estimator for the general class of generalised structured models. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 551 566 Enno Mammen

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:579-5892009-04-18RePEc:oup:biomet

article Cook's (1986) normal curvature measure is useful for sensitivity analysis of model assumptions in statistical models. However, there is no rigorous approach based on the normal curvature for addressing two fundamental issues: to assess the extent of discrepancy between an assumed model and the underlying model from which the data are generated, and to identify suspicious data points for which the discrepancy is most evident. Our purpose is to establish a theoretically sound procedure for resolving these issues for case-weight perturbation under the framework of independent distributions. We show that the local influence measure, Cook's distance and likelihood distance are asymptotically equivalent. A diagnostic procedure, based on local influence, is proposed for evaluating model misspecification and for detecting influential points simultaneously. We analyse two real datasets. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 579 589 Hongtu Zhu

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:469-4792009-04-18RePEc:oup:biomet

article The central subspace and central mean subspace are two important targets of sufficient dimension reduction. We propose a weighted chi-squared test to determine their dimensions based on matrices whose column spaces are exactly equal to the central subspace or the central mean subspace. The asymptotic distribution of the test statistic is obtained. Simulation examples are used to demonstrate the performance of this test. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 469 479 http://hdl.handle.net/10.1093/biomet/asn002 application/pdf Access to full text is restricted to subscribers. Peng Zeng

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:705-7142009-04-18RePEc:oup:biomet

article A simple geometry allows the main properties of matrix approximations used in biplot displays to be developed. It establishes orthogonal components of an analysis of variance, from which different contributions to approximations may be assessed. Particular attention is paid to approximations that share the same singular vectors, in which case the solution space is a convex cone. Two- and three-dimensional approximations are examined in detail and then the geometry is interpreted for different forms of the matrix being approximated. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 705 714 J. C. Gower

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:777-7902009-04-18RePEc:oup:biomet

article This paper is concerned with a general class of observation-driven models for time series of counts whose conditional distributions given past observations and explanatory variables follow a Poisson distribution. These models provide a flexible framework for modelling a wide range of dependence structures. Conditions for stationarity and ergodicity of these processes are established from which the large-sample properties of the maximum likelihood estimators can be derived. Simulations are provided to give additional insight into the finite-sample behaviour of the estimators. Finally an application to a regression model for daily counts of asthma presentations at a Sydney hospital is described. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 777 790 Richard A. Davis

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:135-1522009-04-18RePEc:oup:biomet

article We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are 'proper objective priors' to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full-rank linear models. We extend these priors to deal with general hypotheses in general linear models, not necessarily of full rank. The resulting priors, which we call 'conventional priors', are expressed as a generalization of recently introduced 'partially informative distributions'. The corresponding Bayes factors are fully automatic, easily computed and very reasonable. The methodology is illustrated for the change-point problem and the equality of treatments effects problem. We compare the conventional priors derived for these problems with other objective Bayesian proposals like the intrinsic priors. It is concluded that both priors behave similarly although interesting subtle differences arise. We adapt the conventional priors to deal with nonnested model selection as well as multiple-model comparison. Finally, we briefly address a generalization of conventional priors to nonnormal scenarios. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 135 152 http://hdl.handle.net/10.1093/biomet/asm014 application/pdf Access to full text is restricted to subscribers. M.J. Bayarri Gonzalo García-Donato

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:671-6862009-04-18RePEc:oup:biomet

article Interval-censored lifetime data arise when individuals in a study are inspected intermittently so that a lifetime is observed to lie between two successive times. In settings where only these two times are available, methods exist for nonparametric or parametric estimation of lifetime distributions. However, there has been virtually no discussion of how inspection processes may be estimated or identified. Such estimates are needed if one is to generate interval-censored data by simulation. This paper identifies which aspects of an independent inspection process are estimable from interval-censored data, and shows how to obtain nonparametric estimates. The results allow interval-censored data from any specified distribution to be generated, and give new simulation procedures for estimation or testing. A new omnibus goodness-of-fit test is introduced. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 671 686 http://hdl.handle.net/10.1093/biomet/93.3.671 text/html Access to full text is restricted to subscribers. J. F. Lawless Denise Babineau

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:53-712009-04-18RePEc:oup:biomet

article Recently, pattern-mixture modelling has become a popular tool for modelling incomplete longitudinal data. Such models are under-identified in the sense that, for any drop-out pattern, the data provide no direct information on the distribution of the unobserved outcomes, given the observed ones. One simple way of overcoming this problem, ordinary extrapolation of sufficiently simple pattern-specific models, often produces rather unlikely descriptions; several authors consider identifying restrictions instead. Molenberghs et al. (1998) have constructed identifying restrictions corresponding to missing at random. In this paper, the family of restrictions where drop-out does not depend on future, unobserved observations is identified. The ideas are illustrated using a clinical study of Alzheimer patients. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 53 71 M. G. Kenward

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:35-472009-04-18RePEc:oup:biomet

article We propose a new causal parameter, which is a natural extension of existing approaches to causal inference such as marginal structural models. Modelling approaches are proposed for the difference between a treatment-specific counterfactual population distribution and the actual population distribution of an outcome in the target population of interest. Relevant parameters describe the effect of a hypothetical intervention on such a population and therefore we refer to these models as population intervention models. We focus on intervention models estimating the effect of an intervention in terms of a difference and ratio of means, called risk difference and relative risk if the outcome is binary. We provide a class of inverse-probability-of-treatment-weighted and doubly-robust estimators of the causal parameters in these models. The finite-sample performance of these new estimators is explored in a simulation study. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 35 47 http://hdl.handle.net/10.1093/biomet/asm097 application/pdf Access to full text is restricted to subscribers. Alan E. Hubbard Mark J. van der Laan

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:683-7032009-04-18RePEc:oup:biomet

article We consider regression for response and covariates which are temporal processes observed over intervals. A functional generalised linear model is proposed which includes extensions of standard models in multi-state survival analysis. Simple nonparametric estimators of time-indexed parameters are developed using 'working independence' estimating equations and are shown to be uniformly consistent and to converge weakly to Gaussian processes. The procedure does not require smoothing or a Markov assumption, unlike approaches based on transition intensities. The usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations. Simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy. The estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters, providing novel goodness-of-fit tests. The methodology's practical utility is illustrated in a data analysis. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 683 703 J. P. Fine

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:37-502009-04-18RePEc:oup:biomet

article When an assumption of missing at random is untenable, it becomes necessary to model missing-data indicators, which carry information about the parameters of the complete-data population. Within a given application, however, researchers may believe that some aspects of missingness are ignorable but others are not. We argue that there are two different ways to formalize the notion that only part of the missingness is ignorable. These approaches correspond to assumptions that we call partially missing at random and latently missing at random. We explain these concepts and apply them in a latent-class analysis of survey questions with item nonresponse. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 37 50 http://hdl.handle.net/10.1093/biomet/asn069 application/pdf Access to full text is restricted to subscribers. Ofer Harel Joseph L. Schafer

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:517-5312009-04-18RePEc:oup:biomet

article A conditional method is presented that renders an estimating function insensitive to nuisance parameters. The approach is a generalisation of the conditional score method to a general estimating function context and does not require complete specification of the probability model. We exploit the informal relationship between general estimating functions and score functions to derive simple generalisations of sufficient and partially ancillary statistics, referred to as G-sufficient and G-ancillary statistics, respectively. These two types of statistic are defined in a manner that does not require complete knowledge of the probability model and thus are more suitable for use with estimating functions. If we condition on a G-sufficient statistic for the nuisance parameters, the resulting conditional estimating function is insensitive to nuisance parameters and in particular achieves the plug-in unbiasedness property. Furthermore, if the conditioning argument is also G-ancillary for the parameters of interest, then the conditional estimating function possesses an attractive optimality property. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 517 531 John J. Hanfelt

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:731-7432009-04-18RePEc:oup:biomet

article We consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in Markov chain Monte Carlo. Chan & Geyer (1994) established a central limit theorem for ergodic averages by assuming that the underlying Markov chain is geometrically ergodic and that a simple moment condition is satisfied. While it is relatively straightforward to check Chan & Geyer's conditions, their theorem does not lead to a consistent and easily computed estimate of the variance of the asymptotic normal distribution. Conversely, Mykland et al. (1995) discuss the use of regeneration to establish an alternative central limit theorem with the advantage that a simple, consistent estimator of the asymptotic variance is readily available. However, their result assumes a pair of unwieldy moment conditions whose verification is difficult in practice. In this paper, we show that the conditions of Chan & Geyer's theorem are sufficient to establish the central limit theorem of Mykland et al. This result, in conjunction with other recent developments, should pave the way for more widespread use of the regenerative method in Markov chain Monte Carlo. Our results are illustrated in the context of the slice sampler. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 731 743 James P. Hobert

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:755-7672009-04-18RePEc:oup:biomet

article We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 755 767 Julie L. Yee

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:741-7462009-04-18RePEc:oup:biomet

article The asymptotic variance and robust variance estimators of rate ratios estimated using conditional logistic regression from individually-matched case-control data are derived when the presumed proportional hazards model is misspecified. The robust variance estimators are easily computed using Schoenfeld residuals generated from standard partial likelihood estimation software for failure time data. Simulation studies indicate that the robust variance estimators perform well for typical sizes and that the 'rare disease' version should be adequate for all practical purposes. It was also found that model misspecification must be quite extreme before the model-based, i.e. inverse information, variance is significantly biased and that the robust variance estimators are somewhat more variable than the model-based. We conclude that the model-based variance estimator can be used when model misspecification is not severe. The robust estimator should be used when the presumed model clearly fits the data poorly. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 741 746 Anny Hui Xiang

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:629-6432009-04-18RePEc:oup:biomet

article We propose to smooth the Cholesky decomposition of a raw estimate of a multivariate spectrum, allowing different degrees of smoothness for different elements. The final spectral estimate is reconstructed from the smoothed Cholesky elements, and is consistent and positive definite. More importantly, the Cholesky decomposition matrix of the spectrum can be used as a transfer function in generating time series whose spectrum is identical to the given spectrum at the Fourier frequencies. This not only provides us with much flexibility in simulations, but also allows us to construct bootstrap confidence intervals for the multivariate spectrum by generating bootstrap samples using the Cholesky decomposition of the spectral estimate. A numerical example and an application to electroencephalogram data are used as illustrations. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 629 643 Ming Dai

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:555-5712009-04-18RePEc:oup:biomet

article The support vector machine has been a popular choice of classification method for many applications in machine learning. While it often outperforms other methods in terms of classification accuracy, the implicit nature of its solution renders the support vector machine less attractive in providing insights into the relationship between covariates and classes. Use of structured kernels can remedy the drawback. Borrowing the flexible model-building idea of functional analysis of variance decomposition, we consider multicategory support vector machines with analysis of variance kernels in this paper. An additional penalty is imposed on the sum of weights of functional subspaces, which encourages a sparse representation of the solution. Incorporation of the additional penalty enhances the interpretability of a resulting classifier with often improved accuracy. The proposed method is demonstrated through simulation studies and an application to real data. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 555 571 http://hdl.handle.net/10.1093/biomet/93.3.555 text/html Access to full text is restricted to subscribers. Yoonkyung Lee Yuwon Kim Sangjun Lee Ja-Yong Koo

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:231-2422009-04-18RePEc:oup:biomet

article The aim of this article is to develop optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression. The context is roughly the same as that of a related method by Cook & Setodji (2003), but the new method has several advantages. It is asymptotically optimal in the sense described herein and its test statistic for dimension always has a chi-squared distribution asymptotically under the null hypothesis. Additionally, the optimal method allows tests of predictor effects. A comparison of the two methods is provided. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 231 242 http://hdl.handle.net/10.1093/biomet/asm003 application/pdf Access to full text is restricted to subscribers. Jae Keun Yoo R. Dennis Cook

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:747-7582009-04-18RePEc:oup:biomet

article Higher-order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping, in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family. The optimal test, which is approximated, is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter. A bootstrap procedure that ignores the conditioning is shown to have desirable conditional properties in providing third-order relative accuracy in approximation of p-values associated with the optimal test, in both continuous and discrete models. The bootstrap approach is equivalent to third-order analytical approaches, and is demonstrated in a number of examples to give very accurate approximations even for very small sample sizes. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 747 758 http://hdl.handle.net/10.1093/biomet/asn011 application/pdf Access to full text is restricted to subscribers. Thomas J. Diciccio G. Alastair Young

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:765-7782009-04-18RePEc:oup:biomet

article We deal with strong consistency for Bayesian density estimation. An awkward consequence of inconsistency is described. It is pointed out that consistency at some density f-sub-0 depends on the prior mass assigned to the 'pathological' set of those densities that are close to f-sub-0, in a weak sense, and far apart from f-sub-0, in a Hellinger sense. An analysis of these sets leads to the identification of the notion of 'data tracking'. Specific examples in which this phenomenon cannot occur are discussed. When it can happen, we show how and where things can go wrong, thus providing more intuition about the sources of inconsistency. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 765 778 http://hdl.handle.net/10.1093/biomet/92.4.765 text/html Access to full text is restricted to subscribers. Stephen G. Walker Antonio Lijoi Igor Prunster

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:877-8912009-04-18RePEc:oup:biomet

article We present a multi-phase variant of adaptive cluster sampling which allows the sampler to control the number of measurements of the variable of interest. A first-phase sample is selected using an adaptive cluster sampling design based on an inexpensive auxiliary variable associated with the survey variable. Then the network structure of the adaptive cluster sample is used to select an ordinary one-phase or two-phase subsample of units and the values of the survey variable associated with those units are recorded. The population mean is estimated by either a regression-type estimator or a Horvitz--Thompson-type estimator. The results of a simulation study show good performance of the proposed design, and suggest that in many real situations this design might be preferred to the ordinary adaptive cluster sampling design. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 877 891 http://hdl.handle.net/10.1093/biomet/91.4.877 text/html Access to full text is restricted to subscribers. Martín H. Felix-Medina Steven K. Thompson

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:127-1352009-04-18RePEc:oup:biomet

article The problem of providing lower confidence bounds for the mean improvements of p >= 2 test treatments over a control treatment is considered. The expected average and expected maximum allowances are two criteria for comparing different systems of confidence intervals or bounds. In this paper, lower bounds are derived for the expected average allowance and the expected maximum allowance of Dunnett's simultaneous lower confidence bounds for the p mean improvements. These lower bounds hold for any p >= 2 and any allocation of sample sizes. For p &equals; 2 test treatments, sample allocations are given for which the bounds are achievable. For p &equals; 3 test treatments, a tighter set of bounds is derived which enables easy determination of the sample allocation required to achieve highly efficient designs. A table of the bounds for the expected average and expected maximum allowances and the sample allocation that achieves these bounds is given for p &equals; 2, 3. The theoretical results can easily be adapted to cover upper confidence bounds. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 127 135 http://hdl.handle.net/10.1093/biomet/93.1.127 text/html Access to full text is restricted to subscribers. Steven M. Bortnick Angela M. Dean Thomas J. Santner

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:251-2632009-04-18RePEc:oup:biomet

article When using smoothing splines to estimate a function, the user faces the problem of choosing the smoothing parameter. Several techniques are available for selecting this parameter according to certain optimality criteria. Here, we take a different point of view and we propose a technique for choosing between two alternatives, for example allowing for two different levels of degrees of freedom. The problem is addressed in the framework of a mixed-effects model, whose assumptions ensure that the resulting estimator is unbiased. A likelihood-ratio-type test statistic is proposed, and its exact distribution is derived. Tests of linearity and overall effect follow directly. We then extend this idea to additive models where it provides a more attractive alternative than multi-parameter optimisation, and where it gives exact distributional results that can be used in an analysis-of-deviance-type approach. Examples on real data and a simulation study of level and power complete the paper. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 251 263 Eva Cantoni

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:913-9222009-04-18RePEc:oup:biomet

article In practical applications, it is not uncommon for the hazard functions of two groups to converge with time. One approach that allows for converging hazard functions is the proportional odds model. We develop a procedure for testing the proportional odds assumption when the available data consist of two independent random samples of randomly right-censored lifetimes. Asymptotic normality of the test statistic is proved and the procedure is applied to two well-known datasets. The effective significance level and power of the proposed test are assessed through a simulation study. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 913 922 Jean-Yves Dauxois

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:137-1462009-04-18RePEc:oup:biomet

article Regular fractional factorial designs with clear two-factor interactions provide a useful class of designs that are robust to nonnegligible two-factor interactions. In this paper, the concept of clear two-factor interactions is generalised to orthogonal arrays. The new concept leads to a much wider class of designs robust to nonnegligible two-factor interactions. We study the existence and construction of such designs. The designs we construct have a structure that render themselves particularly attractive in the robust parameter design setting. We also discuss an interesting connection between designs with clear two-factor interactions and mixed orthogonal arrays. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 137 146 http://hdl.handle.net/10.1093/biomet/93.1.137 text/html Access to full text is restricted to subscribers. Boxin Tang

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:367-3782009-04-18RePEc:oup:biomet

article Adaptive designs, which allow the sample size to be modified based on sequentially computed observed treatment differences, have been advocated recently for monitoring clinical trials. Although such methods have a great deal of appeal on the surface, we show that such methods are inefficient and that one can improve uniformly on such adaptive designs using standard group-sequential tests based on the sequentially computed likelihood ratio test statistic. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 367 378 Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:73-842009-04-18RePEc:oup:biomet

article We examine the asymptotic behaviour of confidence regions in identifiable one-dimensional parametric models with smooth likelihood function and information equal to zero at a critical point of the parameter space. Confidence regions are based on inversion of the likelihood ratio test statistic and of some common forms of the score and Wald test statistics. For fixed parameter values other than the critical point, all these statistics have limiting x-super-2-sub-(1) distributions, but for most of them the convergence is not uniform near the critical point. When it is not, confidence regions based on inverting the tests, using the x-super-2-sub-(1) approximation, do not asymptotically have the nominal level. The exception to this lack of locally uniform convergence occurs with the score test standardised by expected, rather than observed, information. For the regions based on the score test standardised by observed information and on the likelihood ratio test, conservative procedures that do not rely on the x-super-2-sub-(1) approximation can be developed, but they are much too conservative near the critical parameter value. The regions based on the Wald tests have asymptotic level less than ½, regardless of the procedure used. Our results suggest that no procedure based solely on the likelihood function will be satisfactory. Whether or not this is the case is an open problem. A simulation study illustrates the results of this paper. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 73 84 Matteo Bottai

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:913-9272009-04-18RePEc:oup:biomet

article The cube method allows the selection of balanced samples on several auxiliary variables with equal or unequal inclusion probabilities. Practical implementation of the cube method has raised questions concerning the selection of a multi-phase balanced sampling design, the rebalancing of an unbalanced sampling design by completing it with another sample, the selection of a balanced sample from an unbalanced sample and the coordination of balanced samples. This paper provides a complete solution of all these problems. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 913 927 http://hdl.handle.net/10.1093/biomet/91.4.913 text/html Access to full text is restricted to subscribers. Yves Tille Anne-Catherine Favre

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:249-2652009-04-18RePEc:oup:biomet

article Hjort & Claeskens (2003) developed an asymptotic theory for model selection, model averaging and subsequent inference using likelihood methods in parametric models, along with associated confidence statements. In this article, we consider a semiparametric version of this problem, wherein the likelihood depends on parameters and an unknown function, and model selection/averaging is to be applied to the parametric parts of the model. We show that all the results of Hjort & Claeskens hold in the semiparametric context, if the Fisher information matrix for parametric models is replaced by the semiparametric information bound for semiparametric models, and if maximum likelihood estimators for parametric models are replaced by semiparametric efficient profile estimators. Our methods of proof employ Le Cam's contiguity lemmas, leading to transparent results. The results also describe the behaviour of semiparametric model estimators when the parametric component is misspecified, and also have implications for pointwise-consistent model selectors. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 249 265 http://hdl.handle.net/10.1093/biomet/asm034 application/pdf Access to full text is restricted to subscribers. Gerda Claeskens Raymond J. Carroll

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:333-3432009-04-18RePEc:oup:biomet

article In a parametric model the maximum likelihood estimator of a parameter of interest &psgr; may be viewed as the solution to the equation l′-sub-p(&psgr;) &equals; 0, where l-sub-p denotes the profile <?Pub Caret>loglikelihood function. It is well known that the estimating function l′-sub-p(&psgr;) is not unbiased and that this bias can, in some cases, lead to poor estimates of &psgr;. An alternative approach is to use the modified profile likelihood function, or an approximation to the modified profile likelihood function, which yields an estimating function that is approximately unbiased. In many cases, the maximum likelihood estimating functions are unbiased under more general assumptions than those used to construct the likelihood function, for example under first- or second-moment conditions. Although the likelihood function itself may provide valid estimates under moment conditions alone, the modified profile likelihood requires a full parametric model. In this paper, modifications to l′-sub-p(&psgr;) are presented that yield an approximately unbiased estimating function under more general conditions. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 333 343 Thomas A. Severini

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:747-7622009-04-18RePEc:oup:biomet

article Right-censored data from a classical case-cohort design and a stratified case-cohort design are considered. In the classical case-cohort design the subcohort is obtained as a simple random sample of the entire cohort, whereas in the stratified design this subcohort is elected by independent Bernoulli sampling with arbitrary selection probabilities. For each design and under a linear regression model, methods for estimating the regression parameters are proposed and analysed. These methods are derived by modifying the linear ranks tests and estimating equations that arise from full-cohort data using methods that are similar to the pseudolikelihood estimating equation that has been used in relative risk regression for these models. The estimators so obtained are shown to be consistent and asymptotically normal. Variance estimation and numerical illustrations are also provided. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 747 762 http://hdl.handle.net/10.1093/biomet/93.4.747 text/html Access to full text is restricted to subscribers. Bin Nan Menggang Yu John D. Kalbfleisch

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:909-9202009-04-18RePEc:oup:biomet

article We discuss intrinsic autoregressions for a first-order neighbourhood on a two-dimensional rectangular lattice and give an exact formula for the variogram that extends known results to the asymmetric case. We obtain a corresponding asymptotic expansion that is more accurate and more general than previous ones and use this to derive the de Wijs variogram under appropriate averaging, a result that can be interpreted as a two-dimensional spatial analogue of Brownian motion obtained as the limit of a random walk in one dimension. This provides a bridge between geostatistics, where the de Wijs process was once the most popular formulation, and Markov random fields, and also explains why statistical analysis using intrinsic autoregressions is usually robust to changes of scale. We briefly describe corresponding calculations in the frequency domain, including limiting results for higher-order autoregressions. The paper closes with some practical considerations, including applications to irregularly-spaced data. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 909 920 http://hdl.handle.net/10.1093/biomet/92.4.909 text/html Access to full text is restricted to subscribers. Julian Besag Debashis Mondal

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:492-4982009-04-18RePEc:oup:biomet

article We use the empirical likelihood method to derive a test and thus a confidence interval based on the rank estimators of the regression coefficient in the accelerated failure time model. Standard chi-squared distributions are used to calculate the p-value and to construct the confidence interval. Simulations and examples show that the chi-squared approximation to the distribution of the log empirical likelihood ratio performs well, and has some advantages over the existing methods. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 492 498 http://hdl.handle.net/10.1093/biomet/92.2.492 text/html Access to full text is restricted to subscribers. Mai Zhou

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:205-2202009-04-18RePEc:oup:biomet

article We suggest a new simple approach for estimation and assessment of covariate effects for the cumulative incidence curve in the competing risks model. We consider a semiparametric regression model where some effects may be time-varying and some may be constant over time. Our estimator can be implemented by standard software. Our simulation study shows that the estimator works well and has finite-sample properties comparable with the subdistribution approach. We apply the method to bone marrow transplant data and estimate the cumulative incidence of death in complete remission following a bone marrow transplantation. Here death in complete remission and relapse are two competing events. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 205 220 http://hdl.handle.net/10.1093/biomet/asm096 application/pdf Access to full text is restricted to subscribers. Thomas H. Scheike Mei-Jie Zhang Thomas A. Gerds

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:1-132009-04-18RePEc:oup:biomet

article A nonparametric approach is developed herein to estimate parameters in nonlinear mixed effects models. Asymptotic properties of the nonparametric maximum likelihood estimators and associated computational algorithms are provided. Empirical Bayes estimators of functionals of the random effects are also developed. Applications to population pharmacokinetics are given. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 1 13 Tze Leung Lai

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:19-292009-04-18RePEc:oup:biomet

article As function of time t, a mean residual life is the remaining life expectancy of a subject given survival up to t. The proportional mean residual life model, proposed by Oakes & Dasu (1990), provides an alternative to the Cox proportional hazards model for studying the association between survival times and covariates. In the presence of censoring, we use counting process theory to develop semiparametric inference procedures for the regression coefficients of the Oakes--Dasu model. Simulation studies and an application to the well-known Veterans' Administration lung cancer survival data are presented. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 19 29 http://hdl.handle.net/10.1093/biomet/92.1.19 text/html Access to full text is restricted to subscribers. Y. Q. Chen S. Cheng

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:791-8072009-04-18RePEc:oup:biomet

article In this paper, we carry out an in-depth theoretical investigation of Bayesian inference for the Cox regression model. We establish necessary and sufficient conditions for posterior propriety of the regression coefficient, β, in Cox's partial likelihood, which can be obtained as the limiting marginal posterior distribution of β through the specification of a gamma process prior for the cumulative baseline hazard and a uniform improper prior for β. We also examine necessary and sufficient conditions for posterior propriety of the regression coefficients, β, using full likelihood Bayesian approaches in which a gamma process prior is specified for the cumulative baseline hazard. We examine characterisation of posterior propriety under completely observed data settings as well as for settings involving missing covariates. Latent variables are introduced to facilitate a straightforward Gibbs sampling scheme in the Bayesian computation. A real dataset is presented to illustrate the proposed methodology. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 791 807 http://hdl.handle.net/10.1093/biomet/93.4.791 text/html Access to full text is restricted to subscribers. Ming-Hui Chen Joseph G. Ibrahim Qi-Man Shao

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:555-5712009-04-18RePEc:oup:biomet

article When we estimate the population total for a survey variable or variables, calibration forces the weighted estimates of certain covariates to match known or alternatively estimated population totals called benchmarks. Calibration can be used to correct for sample-survey nonresponse, or for coverage error resulting from frame undercoverage or unit duplication. The quasi-randomization theory supporting its use in nonresponse adjustment treats response as an additional phase of random sampling. The functional form of a quasi-random response model is assumed to be known, its parameter values estimated implicitly through the creation of calibration weights. Unfortunately, calibration depends upon known benchmark totals while the covariates in a plausible model for survey response may not be the benchmark covariates. Moreover, it may be prudent to keep the number of covariates in a response model small. We use calibration to adjust for nonresponse when the benchmark model and covariates may differ, provided the number of the former is at least as great as that of the latter. We discuss the estimation of a total for a vector of survey variables that do not include the benchmark covariates, but that may include some of the model covariates. We show how to measure both the additional asymptotic variance due to the nonresponse in a calibration-weighted estimator and the full asymptotic variance of the estimator itself. All variances are determined with respect to the randomization mechanism used to select the sample, the response model generating the subset of sample respondents, or both. Data from the U.S. National Agricultural Statistical Service's 2002 Census of Agriculture and simulations are used to illustrate alternative adjustments for nonresponse. The paper concludes with some remarks about adjustment for coverage error. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 555 571 http://hdl.handle.net/10.1093/biomet/asn022 application/pdf Access to full text is restricted to subscribers. Ted Chang Phillip S. Kott

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:553-5662009-04-18RePEc:oup:biomet

article Parsimonious modelling of the within-subject covariance structure while heeding its positive-definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse Wishart priors. Our priors offer many advantages with regard to elicitation, positive definiteness, computations using Gibbs sampling, shrinking covariances toward a particular structure with considerable flexibility, and modelling covariances using covariates. Bayesian estimation methods are developed and the results are compared using two simulation studies. These simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 553 566 Michael J. Daniels

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:237-2422009-04-18RePEc:oup:biomet

article In medical research, investigators often wish to characterize the distributions of remaining lifetimes. While nonparametric analyses of residual life distributions have been widely studied with independently right-censored data, residual life analysis has not been examined in the competing risks setting, with multiple, potentially dependent, failure types. We define the cause-specific residual life distribution as the residual cumulative incidence function conditionally on survival to a given time. Because of the improper form of the cause-specific distribution, the mean cause-specific residual lifetime does not exist, theoretically. We develop nonparametric inferences for the cause-specific residual life function and its corresponding quantiles, which may exist. Theoretical justification, including uniform consistency and weak convergence, is established. Simulation studies and a breast cancer data analysis demonstrate the practical utility of the methods. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 237 242 http://hdl.handle.net/10.1093/biomet/asn063 application/pdf Access to full text is restricted to subscribers. J.-H. Jeong J. P. Fine

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:509-5242009-04-18RePEc:oup:biomet

article We present a method for multiple hypothesis testing that maintains control of the false discovery rate while incorporating prior information about the hypotheses. The prior information takes the form of p-value weights. If the assignment of weights is positively associated with the null hypotheses being false, the procedure improves power, except in cases where power is already near one. Even if the assignment of weights is poor, power is only reduced slightly, as long as the weights are not too large. We also provide a similar method for controlling false discovery exceedance. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 509 524 http://hdl.handle.net/10.1093/biomet/93.3.509 text/html Access to full text is restricted to subscribers. Christopher R. Genovese Kathryn Roeder Larry Wasserman

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:971-9742009-04-18RePEc:oup:biomet

article Rubin & Schenker (1986) proposed the approximate Bayesian bootstrap, a two-stage resampling procedure, as a method of creating multiple imputations when missing data are ignorable. Kim (2002) showed that the multiple imputation variance estimator is biased for moderate sample sizes when this method is used. To reduce the bias, Kim (2002) proposed modifying the number of samples drawn at the first stage of the Bayesian bootstrap procedure. In this note, we suggest an alternative method for reducing the bias via a simple correction factor applied to the standard multiple imputation variance estimate. The proposed correction is more easily implemented and more efficient than the procedure proposed by Kim (2002). Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 971 974 http://hdl.handle.net/10.1093/biomet/92.4.971 text/html Access to full text is restricted to subscribers. Michael Parzen Stuart R. Lipsitz Garrett M. Fitzmaurice

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:249-2502009-04-18RePEc:oup:biomet

article 1 2005 92 March Biometrika 249 250 http://hdl.handle.net/10.1093/biomet/92.1.249-a text/html Access to full text is restricted to subscribers. K. V. Mardia F. L. Bookstein I. J. Moreton

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:667-6782009-04-18RePEc:oup:biomet

article We consider statistical inference for additive partial linear models when the linear covariate is measured with error. We propose attenuation-to-correction and simulation-extrapolation, simex, estimators of the parameter of interest. It is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing. This is an advantage of our estimator over existing backfitting-based estimators for semiparametric additive models which require undersmoothing of the nonparametric component in order for the estimator of the parametric component to be root-n consistent. This feature stems from a decrease of the bias of the resulting estimator, which is appropriately derived using a profile procedure. A similar characteristic in semiparametric partially linear models was obtained by Wang et al. (2005). We also discuss the asymptotics of the proposed simex approach. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are applied to a dataset from a semen study. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 667 678 http://hdl.handle.net/10.1093/biomet/asn024 application/pdf Access to full text is restricted to subscribers. Hua Liang Sally W. Thurston David Ruppert Tatiyana Apanasovich Russ Hauser

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:470-4772009-04-18RePEc:oup:biomet

article The approximate Bayesian bootstrap is suggested by Rubin & Schenker (1986) as a way of generating multiple imputations when the original sample can be regarded as independently and identically distributed and the response mechanism is ignorable. We investigate the finite sample properties of the variance estimator when the approximate Bayesian bootstrap method is used and show that the bias is not negligible for moderate sample sizes. A modification of the method is proposed for reducing the bias of the variance estimator. The proposed method is asymptotically equivalent to the approximate Bayesian bootstrap method but has better finite sample properties. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 470 477 J. K. Kim

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:385-3972009-04-18RePEc:oup:biomet

article In a case-augmented study, measurements on a random sample from a population are augmented by information from an independent sample of cases, that is units with some characteristic of interest. We show that inferences about the effect of the covariates on the probability of being a case can be made by fitting a modified prospective likelihood. We also show that this procedure is fully efficient. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 385 397 http://hdl.handle.net/10.1093/biomet/93.2.385 text/html Access to full text is restricted to subscribers. A. J. Lee A. J. Scott C. J. Wild

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:415-4362009-04-18RePEc:oup:biomet

article We study the asymptotic behaviour of penalized spline estimators in the univariate case. We use B-splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya--Watson kernel estimators with 'equivalent' kernels depending upon m. The equivalent kernels we obtain for penalized splines are the same as those found by Silverman for smoothing splines. The asymptotic distribution of the penalized spline estimator is Gaussian and we give simple expressions for the asymptotic mean and variance. Provided that it is fast enough, the rate at which the number of knots converges to infinity does not affect the asymptotic distribution. The optimal rate of convergence of the penalty parameter is given. Penalized splines are not design-adaptive. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 415 436 http://hdl.handle.net/10.1093/biomet/asn010 application/pdf Access to full text is restricted to subscribers. Yingxing Li David Ruppert

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:875-8912009-04-18RePEc:oup:biomet

article We consider the problem of estimating the regression coefficients in a competing risks model, where the relationship between the cause-specific hazard for the cause of interest and covariates is described using linear transformation models and when cause of failure is missing at random for a subset of individuals. Using the theory of Robins et al. (1994) for missing data problems and the approach of Chen et al. (2002) for estimating regression coefficients for linear transformation models, we derive augmented inverse probability weighted complete-case estimators for the regression coefficients that are doubly robust. Simulations demonstrate the relevance of the theory in finite samples. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 875 891 http://hdl.handle.net/10.1093/biomet/92.4.875 text/html Access to full text is restricted to subscribers. Guozhi Gao Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:399-4142009-04-18RePEc:oup:biomet

article We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau tests, is designed to check whether or not the estimated models are adequate. The simulation experiments give further support to our model and the results for the absolute returns of the Dow Jones Industrial Average Index daily closing price demonstrate their usefulness in modelling time series exhibiting the features of long memory, conditional heteroscedasticity and heavy tails. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 399 414 http://hdl.handle.net/10.1093/biomet/asn014 application/pdf Access to full text is restricted to subscribers. Guodong Li Wai Keung Li

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:719-7232009-04-18RePEc:oup:biomet

article Motivated by problems in molecular biology and molecular physics, we propose a five-parameter torus analogue of the bivariate normal distribution for modelling the distribution of two circular random variables. The conditional distributions of the proposed distribution are von Mises. The marginal distributions are symmetric around their means and are either unimodal or bimodal. The type of shape depends on the configuration of parameters, and we derive the conditions that ensure a specific shape. The utility of the proposed distribution is illustrated by the modelling of angular variables in a short linear peptide. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 719 723 Harshinder Singh

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:723-7332009-04-18RePEc:oup:biomet

article With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest posterior density. These asymptotics, in turn, characterise members of the class that allow approximate frequentist validity of such sets. It is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 723 733 http://hdl.handle.net/10.1093/biomet/93.3.723 text/html Access to full text is restricted to subscribers. Kai-Tai Fang Rahul Mukerjee

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:977-9842009-04-18RePEc:oup:biomet

article We consider kernel-type methods for the estimation of a density on 0,1 which eschew explicit boundary correction. We propose using kernels that are symmetric in their two arguments; these kernels are conditional densities of bivariate copulas. We give asymptotic theory for the version of the new estimator using Gaussian copula kernels and report on simulation comparisons of it with the beta-kernel density estimator of Chen ([1]). We also provide automatic bandwidth selection in the form of 'rule-of-thumb' bandwidths for both estimators. As well as its competitive integrated squared error performance, advantages of the new approach include its greater range of possible values at 0 and 1, the fact that it is a bona fide density and that the individual kernels and resulting estimator are comprehensible in terms of a single simple picture. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 977 984 http://hdl.handle.net/10.1093/biomet/asm068 application/pdf Access to full text is restricted to subscribers. M.C. Jones D.A. Henderson

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:263-2752009-04-18RePEc:oup:biomet

article We present a simple sample-size formula for weighted log-rank statistics applied to clustered survival data with variable cluster sizes and arbitrary treatment assignments within clusters. This formula is based on the asymptotic normality of weighted log-rank statistics under certain local alternatives in the clustered data context. We also provide consistent variance estimators. The derived sample-size formula reduces to Schoenfeld's (1983) formula for cases of no clustering or independence within clusters. Simulation results verify control of the Type I error and accuracy of the sample-size formula. Use of the sample-size formula in an event-driven clinical trial design is illustrated using data from the Early Treatment Diabetic Retinopathy Study. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 263 275 Ronald E. Gangnon

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:299-3142009-04-18RePEc:oup:biomet

article There has been much research on analysing multivariate failure times, but little that has accommodated failures that arise in the presence of a competing failure process. This paper studies the problem of describing associations among times to such failures. It proposes a modified conditional hazard ratio measure of association that is tailored to competing risks data, develops frailty models and a nonparametric method for describing the proposed measure, and contrasts estimation by proposed methods with the 'standard' of treating competing risks as independently censoring failure times due to targeted causes. The methods are investigated on simulated and real data. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 299 314 Karen Bandeen-Roche

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:847-8582009-04-18RePEc:oup:biomet

article We use the quasilikelihood concept to propose an estimating equation for spatial data with correlation across the study region in a multi-dimensional space. With appropriate mixing conditions, we develop a central limit theorem for a random field under various L_p metrics. The consistency and asymptotic normality of quasilikelihood estimators can then be derived. We also conduct simulations to evaluate the performance of the proposed estimating equation, and a dataset from East Lansing Woods is used to illustrate the method. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 847 858 http://hdl.handle.net/10.1093/biomet/asn046 application/pdf Access to full text is restricted to subscribers. Pei-Sheng Lin

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:643-6542009-04-18RePEc:oup:biomet

article In this paper we introduce a new stochastic variant of the EM algorithm. The algorithm combines the principle of multiple imputation and the theory of simulated annealing to deal with cases where the E-step and the M-step can be intractable or numerically inefficient. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 643 654 Carlo Gaetan

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:315-3312009-04-18RePEc:oup:biomet

article Logistic regression is often used to find a linear combination of covariates which best discriminates between two groups or populations. The ROC, receiver operating characteristic, curve is a good way of assessing the performance of the resulting score, but using the same data both to fit the score and to calculate its ROC leads to an over-optimistic estimate of the performance which the score would give if it were to be validated on a sample of future cases. The paper studies the extent of this overestimation, and suggests a shrinkage correction for the ROC curve itself and for the area under the curve. The correction is consistent with Efron's formula for the bias in the error rate of a binary prediction rule. Two medical examples are discussed. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 315 331 J. B. Copas

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:327-3392009-04-18RePEc:oup:biomet

article For a statistical model with data, likelihood for the scalar or vector full parameter &thgr;, of dimension p say, is typically well defined and easily computed. In this paper, we investigate likelihood for a component parameter &psgr;(&thgr;) of dimension d < p and make use of the recent likelihood theory that has been successful in producing highly accurate third-order p-values for scalar parameters of continuous models. The theory leads under moderate regularity to a definitive third-order determination of likelihood for a component parameter &psgr;(&thgr;) of dimension d, where 1 <= d <= p. We use the simple location model on the plane with standard normal errors to motivate the development. The example exhibits most of the key characteristics of the general case and the recent theory then extends the determination of likelihood to the general context. For the scalar interest parameter case with d &equals; 1, the usual determinations are typically of second-order accuracy; the example indicates how the new determination achieves third-order accuracy. The implementation is straightforward and uses familiar ingredients to other determinations, such as the full maximum likelihood value &thgr;ˆ, the constrained value &thgr;˜-sub-&psgr; given &psgr;(&thgr;) &equals; &psgr;, and the observed information j-sub-&lgr;&lgr;(&thgr;ˆ-sub-&psgr;) for a complementing nuisance parameter &lgr;(&thgr;). It does however require a special version of the nuisance information j-sub-&lgr;&lgr;(&thgr;ˆ-sub-&psgr;), a version calibrated relative to a symmetric choice of the exponential-type reparameterisation &phgr;(&thgr;) underlying the recent theory, but this is easily computed. Various examples are given and the motivating example is discussed in detail. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 327 339 D. A. S. Fraser

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:401-4092009-04-18RePEc:oup:biomet

article The maximum likelihood estimator of the variance components in a linear model can be biased downwards. Restricted maximum likelihood (REML) corrects this problem by using the likelihood of a set of residual contrasts and is generally considered superior. However, this original restricted maximum likelihood definition does not directly extend beyond linear models. We propose a REML-type estimator for generalised linear mixed models by correcting the bias in the profile score function of the variance components. The proposed estimator has the same consistency properties as the maximum likelihood estimator if the number of parameters in the mean and variance components models remains fixed. However, the estimator of the variance components has a smaller finite sample bias. A simulation study with a logistic mixed model shows <?Pub Caret>that the proposed estimator is effective in correcting the downward bias in the maximum likelihood estimator. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 401 409 J. G. Liao

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:47-572009-04-18RePEc:oup:biomet

article Probability matching priors are priors for which the posterior probabilities of certain specified sets are exactly or approximately equal to their coverage probabilities. These priors arise as solutions of partial differential equations that may be difficult to solve, either analytically or numerically. Recently Levine & Casella (2003) presented an algorithm for the implementation of probability matching priors for an interest parameter in the presence of a single nuisance parameter. In this paper we develop a local implementation that is very much more easily computed. A local probability matching prior is a data-dependent approximation to a probability matching prior and is such that the asymptotic order of approximation of the frequentist coverage probability is not degraded. We illustrate the theory with a number of examples, including three discussed in Levine & Casella (2003). Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 47 57 http://hdl.handle.net/10.1093/biomet/92.1.47 text/html Access to full text is restricted to subscribers. Trevor J. Sweeting

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:61-702009-04-18RePEc:oup:biomet

article The constant-sum property given in Oller et al. (2004) for censoring models justifies the use of a simplified likelihood to obtain the nonparametric maximum likelihood estimator of the lifetime distribution. In this paper we study the relevance of the constant-sum property in the identifiability of the lifetime distribution. We show that the lifetime distribution is not identifiable outside the class of constant-sum models. We also show that the lifetime probabilities assigned to the observable intervals are identifiable inside the class of constant-sum models. We illustrate all these notions with several examples. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 61 70 http://hdl.handle.net/10.1093/biomet/asm002 application/pdf Access to full text is restricted to subscribers. Ramon Oller Guadalupe Gómez M. Luz Calle

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:111-1282009-04-18RePEc:oup:biomet

article <?Pub Caret> A global smoothing procedure is developed using basis function approximations for estimating the parameters of a varying-coefficient model with repeated measurements. Inference procedures based on a resampling subject bootstrap are proposed to construct confidence regions and to perform hypothesis testing. Conditional biases and variances of our estimators and their asymptotic consistency are developed explicitly. Finite sample properties of our procedures are investigated through a simulation study. Application of the proposed approach is demonstrated through an example in epidemiology. In contrast to the existing methods, this approach applies whether or not the covariates are time-invariant and does not require binning of the data when observations are sparse at distinct observation times. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 111 128 Jianhua Z. Huang

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:228-2342009-04-18RePEc:oup:biomet

article Jones (1989) has pointed out that piecewise linear interpolated kernel density estimators on a sufficiently fine grid can be visually indistinguishable from the true density. A simple device, the kernel polygon, is proposed for eliminating the evaluation of the normalisation constant of the estimator while retaining its property of being a density function as well as providing practical advantages. The class of uniform and linear kernels of the kernel polygons is given. Finally, we present a simulation study and a real data example in which we compare bandwidth selectors for the kernel polygons. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 228 234 http://hdl.handle.net/10.1093/biomet/93.1.228 text/html Access to full text is restricted to subscribers. Chien-Tai Lin Jyh-Shyang Wu Chia-Hung Yen

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:539-5532009-04-18RePEc:oup:biomet

article The validity of design-based inference is not dependent on any model assumption. However, it is well known that estimators derived through design-based theory may be inefficient for the estimation of population totals when the design weights are weakly related to the variables of interest and have widely dispersed values. We propose estimators that have the potential to improve the efficiency of any estimator derived under the design-based theory. Our main focus is limited to the improvement of the Horvitz--Thompson estimator, but we also discuss the extension to calibration estimators. The new estimators are obtained by smoothing design or calibration weights using an appropriate model. Our approach to inference requires the modelling of only one variable, the weight, and it leads to a single set of smoothed weights in multipurpose surveys. This is to be contrasted with other model-based approaches, such as the prediction approach, in which it is necessary to postulate and validate a model for each variable of interest leading potentially to variable-specific sets of weights. Our proposed approach is first justified theoretically and then evaluated through a simulation study. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 539 553 http://hdl.handle.net/10.1093/biomet/asn028 application/pdf Access to full text is restricted to subscribers. Jean-François Beaumont

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:279-2882009-04-18RePEc:oup:biomet

article The Latin hypercube design is a popular choice of experimental design when computer simulation is used to study a physical process. These designs guarantee uniform samples for the marginal distribution of each single input. A number of methods have been proposed for extending the uniform sampling to higher dimensions.We show how to construct Latin hypercube designs in which all main effects are orthogonal. Our method can also be used to construct Latin hypercube designs with low correlation of first-order and second-order terms. Our method generates orthogonal Latin hypercube designs that can include many more factors than those proposed by Ye (1998). Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 279 288 http://hdl.handle.net/10.1093/biomet/93.2.279 text/html Access to full text is restricted to subscribers. David M. Steinberg Dennis K. J. Lin

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:289-3022009-04-18RePEc:oup:biomet

article Blocking of two-level factorial designs is considered for block sizes 2 and 4 using the method of fractional partial confounding. A-, D- and E-optimal designs are obtained for block size 2 within the class of orthogonal designs for which main effects and two-factor interactions are all orthogonal to each other before allowing for blocking. A-, D- and E-optimal designs are obtained for block size 4 within the class of orthogonal designs with main effects orthogonal to blocks. The designs obtained also have other favourable properties including orthogonal estimation of effects and orthogonality to superblocks. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 289 302 http://hdl.handle.net/10.1093/biomet/93.2.289 text/html Access to full text is restricted to subscribers. Neil A. Butler

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:197-2122009-04-18RePEc:oup:biomet

article A main objective in clinical trials is to find the best treatment in a given finite class of competing treatments and then to show superiority of this treatment against a control treatment. The traditional procedure estimates the best treatment in a first trial. Then in an independent second trial superiority of this treatment, estimated as best in the first trial, is to be shown against the control treatment by a size α test. In this paper we investigate these two trials of this traditional procedure as a two-stage test procedure. Additionally we introduce competing two-stage group-sequential test procedures. Then we derive formulae for the expected number of patients. These formulae depend on unknown parameters. When we have a prior for the unknown parameters we can determine the two-stage test procedure of size α and power β that is optimal, in that it needs a minimal number of observations. The results are illustrated by a numerical example, which indicates the superiority of the group-sequential procedures. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 197 212 http://hdl.handle.net/10.1093/biomet/92.1.197 text/html Access to full text is restricted to subscribers. Wolfgang Bischoff Frank Miller

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:999-10052009-04-18RePEc:oup:biomet

article We show that, when the three-way association level among the three binary variables, X, U₁ and U₂ is fixed, D_P &equals; pr(X &equals; 1¦U₁ &equals; 1) - pr(X &equals; 1¦U₁ &equals; 0) increases as the cross-product ratio of U₁ and U₂ increases under the assumption that X is positively associated with U₁ and U₂. We then discuss some implications of this property. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 999 1005 http://hdl.handle.net/10.1093/biomet/asm075 application/pdf Access to full text is restricted to subscribers. Stephen E. Fienberg Sung-Ho Kim

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:893-9072009-04-18RePEc:oup:biomet

article We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full proportion of false null hypotheses is discussed and compared to other estimators. The proposed estimator is shown to deliver a tight probabilistic lower bound for the number of false null hypotheses in a multiple testing situation even under strong dependence between test statistics. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 893 907 http://hdl.handle.net/10.1093/biomet/92.4.893 text/html Access to full text is restricted to subscribers. Nicolai Meinshausen Peter Buhlmann

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:471-4772009-04-18RePEc:oup:biomet

article This paper considers group testing when the probability of response is increasing across the levels of an observed covariate. We illustrate how previously known results in order-restricted inference can be extended to situations wherein data are collected according to a group-testing protocol, and we derive maximum likelihood estimators for proportions under the increasing order restriction and group-testing model. Finally, we show how the use of group testing can dramatically reduce the bias and mean squared error of isotonic regression estimators obtained from one-at-a-time testing. These proposed methods are illustrated using data from an observational HIV study conducted in Houston, Texas. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 471 477 Joshua M. Tebbs

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:291-3032009-04-18RePEc:oup:biomet

article Sequentially ordered multivariate failure time data are often observed in biomedical studies and inter-event, or gap, times are often of interest. Generally, standard hazard regression methods cannot be applied to the gap times because of identifiability issues and induced dependent censoring. We propose estimating equations for fitting proportional hazards regression models to the gap times. Model parameters are shown to be consistent and asymptotically normal. Simulation studies reveal the appropriateness of the asymptotic approximations in finite samples. The proposed methods are applied to renal failure data to assess the association between demographic covariates and both time until wait-listing and time from wait-listing to kidney transplantation. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 291 303 Douglas E. Schaubel

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:105-1182009-04-18RePEc:oup:biomet

article Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to achieve the optimal nonparametric convergence rateestablished by Stone (1982). Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 105 118 http://hdl.handle.net/10.1093/biomet/92.1.105 text/html Access to full text is restricted to subscribers. Peter Hall J. D. Opsomer

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:921-9372009-04-18RePEc:oup:biomet

article A semiparametric regression model for longitudinal data is considered. The empirical likelihood method is used to estimate the regression coefficients and the baseline function, and to construct confidence regions and intervals. It is proved that the maximum empirical likelihood estimator of the regression coefficients achieves asymptotic efficiency and the estimator of the baseline function attains asymptotic normality when a bias correction is made. Two calibrated empirical likelihood approaches to inference for the baseline function are developed. We propose a groupwise empirical likelihood procedure to handle the inter-series dependence for the longitudinal semiparametric regression model, and employ bias correction to construct the empirical likelihood ratio functions for the parameters of interest. This leads us to prove a nonparametric version of Wilks' theorem. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. A simulation compares the empirical likelihood and normal-based methods in terms of coverage accuracies and average areas/lengths of confidence regions/intervals. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 921 937 http://hdl.handle.net/10.1093/biomet/asm066 application/pdf Access to full text is restricted to subscribers. Liugen Xue Lixing Zhu

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:173-1822009-04-18RePEc:oup:biomet

article Asymptotic multivariate normal approximations to the joint distributions of edge exclusion test statistics for saturated graphical Gaussian models are derived. Non-signed and signed square-root versions of the likelihood ratio, Wald and score test statistics are considered. Noncentral chi-squared approximations are also considered for the non-signed versions. These approximations are used to estimate the power of edge exclusion tests and an example is presented. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 173 182 http://hdl.handle.net/10.1093/biomet/92.1.173 text/html Access to full text is restricted to subscribers. M. Fátima Salgueiro Peter W. F. Smith John W. McDonald

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:249-2492009-04-18RePEc:oup:biomet

article 1 2005 92 March Biometrika 249 249 http://hdl.handle.net/10.1093/biomet/92.1.249 text/html Access to full text is restricted to subscribers. J. T. Kent K. V. Mardia

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:19-362009-04-18RePEc:oup:biomet

article Causal approaches based on the potential outcome framework provide a useful tool for addressing noncompliance problems in randomized trials. We propose a new estimator of causal treatment effects in randomized clinical trials with noncompliance. We use the empirical likelihood approach to construct a profile random sieve likelihood and take into account the mixture structure in outcome distributions, so that our estimator is robust to parametric distribution assumptions and provides substantial finite-sample efficiency gains over the standard instrumental variable estimator. Our estimator is asymptotically equivalent to the standard instrumental variable estimator, and it can be applied to outcome variables with a continuous, ordinal or binary scale. We apply our method to data from a randomized trial of an intervention to improve the treatment of depression among depressed elderly patients in primary care practices. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 19 36 http://hdl.handle.net/10.1093/biomet/asn056 application/pdf Access to full text is restricted to subscribers. Jing Cheng Dylan S. Small Zhiqiang Tan Thomas R. Ten Have

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:27-432009-04-18RePEc:oup:biomet

article By extending Schwarz's (1978) basic idea we derive a Bayesian information criterion which enables us to evaluate models estimated by the maximum penalised likelihood method or the method of regularisation. The proposed criterion is applied to the choice of smoothing parameters and the number of basis functions in radial basis function network models. Monte Carlo experiments were conducted to examine the performance of the nonlinear modelling strategy of estimating the weight parameters by regularisation and then determining the adjusted parameters by the Bayesian information criterion. The simulation results show that our modelling procedure performs well in various situations. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 27 43 Sadanori Konishi

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:359-3742009-04-18RePEc:oup:biomet

article Motivated by applications in high-dimensional settings, we suggest a test of the hypothesis H-sub-0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may be multivariate or infinite-dimensional, in the latter case representing, for example, the distributions of random functions from one Euclidean space to another. Our test uses a measure of distance between data. This measure should be symmetric but need not satisfy the triangle inequality, so it is not essential that it be a metric. The test is based on ranking the pooled dataset, with respect to the distance and relative to any fixed data value, and repeating this operation for each fixed datum. A permutation argument enables a critical point to be chosen such that the test has concisely known significance level, conditional on the set of all pairwise distances. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 359 374 Peter Hall

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:529-5382009-04-18RePEc:oup:biomet

article We present a new, nonparametric Bayesian method for multiple imputation of partially observed data for which the pattern of missingness is arbitrary and the data are missing at random with ignorable nonresponse with respect to the model specification. Motivation for the method is provided, followed by an overview of Pólya trees and their application to multiple imputation, and a comparison of the new method to existing approaches is presented. The method is illustrated on a dataset of colleges and universities in the United States. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 529 538 Susan M. Paddock

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:477-4842009-04-18RePEc:oup:biomet

article The weighted least absolute deviations estimator is studied for an AR(1) process with ARCH(1) errors &epsiv;-sub-t. Unlike for the quasi maximum likelihood estimator, the estimator's, limiting distribution is shown to be normal even when E(&epsiv;-sub-t-super-4) &equals; ∞. Furthermore, the estimator can be applied to examine the symmetry of the density of &epsiv;-sub-t and to estimate the quantity E(log |α &plus; λ-super-½ &epsiv;-sub-t|), which are of crucial importance for conducting asymptotic inference for quasi maximum likelihood estimators and weighted least absolute deviations estimators. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 477 484 http://hdl.handle.net/10.1093/biomet/92.2.477 text/html Access to full text is restricted to subscribers. Ngai Hang Chan Liang Peng

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:863-8732009-04-18RePEc:oup:biomet

article This paper studies the coherence conditions of dose-finding methods in the context of phase I clinical trials, where the objective is to estimate a targeted quantile of the unknown dose-toxicity curve. Most phase I methods are outcome-adaptive, and thus escalate or de-escalate doses for future patients based on the previous observations. An escalation for a new patient is said to be coherent only when the previous patient does not show sign of toxicity. Likewise, a de-escalation is coherent only when a toxic outcome has just been seen. The coherence conditions, motivated by ethical concerns in trial conduct, are satisfied by many statistical designs in the literature, but not by some commonly used modifications of the methods. This paper shows examples in which coherence is violated, and discusses how the coherence principles may be applied to calibrate a two-stage design and to deal with situations with delayed toxicity. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 863 873 http://hdl.handle.net/10.1093/biomet/92.4.863 text/html Access to full text is restricted to subscribers. Ying Kuen Cheung

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:345-3622009-04-18RePEc:oup:biomet

article This paper is concerned with estimation of the threshold parameter R-sub-* for a stochastic model for the spread of a susceptible → infective → removed epidemic among a closed, finite population that contains several types of individual and is partitioned into households. It turns out that R-sub-* cannot be estimated consistently from final outcome data, so a Perron--Frobenius argument is used to obtain sharp lower and upper bounds for R-sub-*, which can be estimated consistently. Determining the allocation of vaccines that reduces the upper bound for R-sub-* to its threshold value of one, thus preventing the occurrence of a major outbreak, with minimum vaccine coverage is shown to be a linear programming problem. The estimates of R-sub-*, before and after vaccination, and of the secure vaccination coverage, i.e. the proportion of individuals that have to be vaccinated to reduce the upper bound for R-sub-* to 1 assuming an optimal vaccination scheme, are equipped with standard errors, thus yielding conservative confidence bounds for these key epidemiological parameters. The methodology is illustrated by application to data on influenza outbreaks in Tecumseh, Michigan. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 345 362 Frank G. Ball

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:965-9702009-04-18RePEc:oup:biomet

article The concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models. We derive an analytical expression for the concordance probability in the Cox proportional hazards model. The proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times. For this reason it is asymptotically unbiased, unlike Harrell's c-index based on informative pairs. The asymptotic distribution of the concordance probability estimate is derived using U-statistic theory and the methodology is applied to a predictive model in lung cancer. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 965 970 http://hdl.handle.net/10.1093/biomet/92.4.965 text/html Access to full text is restricted to subscribers. Mithat Gonen Glenn Heller

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:149-1582009-04-18RePEc:oup:biomet

article A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 149 158 http://hdl.handle.net/10.1093/biomet/92.1.149 text/html Access to full text is restricted to subscribers. B. M. Brown You-Gan Wang

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:965-9752009-04-18RePEc:oup:biomet

article Holm's method and Hochberg's method for multiple testing can be viewed as step-down and step-up versions of the Bonferroni test. We show that both are special cases of partition testing. The difference is that, while Holm's method tests each partition hypothesis using the largest order statistic, setting a critical value based on the Bonferroni inequality, Hochberg's method tests each partition hypothesis using all the order statistics, setting a series of critical values based on Simes' inequality. Geometrically, Hochberg's step-up method 'cuts corners' off the acceptance regions of Holm's step-down method by making assumptions on the joint distribution of the test statistics. As can be expected, partition testing making use of the joint distribution of the test statistics is more powerful than partition testing using probabilistic inequalities. Thus, if the joint distribution of the test statistics is available, through modelling for example, we recommend partition step-down testing, setting exact critical values based on the joint distribution. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 965 975 http://hdl.handle.net/10.1093/biomet/asm067 application/pdf Access to full text is restricted to subscribers. Yifan Huang Jason C. Hsu

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:277-2902009-04-18RePEc:oup:biomet

article We analyse doubly censored data using semiparametric transformation models. We provide inference procedures for the regression parameters and derive the asymptotic distributions of the proposed estimators. Procedures for model checking and model selection are also discussed. We illustrate our approach with a viral-load dataset from a recent AIDS clinical trial. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 277 290 T. Cai

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:127-1372009-04-18RePEc:oup:biomet

article Nuisance parameters do not pose any problems in Bayesian inference as marginalisation allows for study of the posterior distribution solely in terms of the parameter of interest. However, no general solution is available for removing nuisance parameters under the frequentist paradigm. In this paper, we merge the two approaches to construct a general procedure for frequentist elimination of nuisance parameters through the use of matching priors. In particular, we perform Bayesian marginalisation with respect to a prior distribution under which posterior inferences have approximate frequentist validity. Matching priors are constructed as solutions to a partial differential equation. Unfortunately, except in simple cases, these partial differential equations do not yield to analytical nor even standard numerical methods of solution. We present a numerical&sol;Monte Carlo algorithm for obtaining the matching prior, in general, as a solution to the appropriate partial differential equation and draw posterior inferences. To be specific, we develop an automated routine through an implementation of the Metropolis--Hastings algorithm for deriving frequentist valid inferences via the matching prior. We illustrate our results in the contexts of fitting random effects models, fitting logistic regression models and fitting teratological data by beta-binomial models. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 127 137 Richard A. Levine

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:629-6412009-04-18RePEc:oup:biomet

article In this paper, we establish both naive and formal Bayesian justifications of Cox's (1975) partial likelihood and its various modifications. We extend the original work of Kalbfieisch (1978), who showed that the partial likelihood is a limiting marginal posterior under noninformative priors for baseline hazards. We extend the result to scenarios with time-dependent covariates and time-varying regression parameters. We establish results for continuous time as well as grouped survival data. In addition, we present a Bayesian justification of a modified partial likelihood for handling ties. We also present tools for simplification of the Gibbs sampling algorithm for implementing partial likelihood based Bayesian inference in various practical applications. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 629 641 Debajyoti Sinha

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:245-2502009-04-18RePEc:oup:biomet

article We prove the conjecture that the generalised inverse Gaussian distribution is positively skew. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 245 250 Truc T. Nguyen

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:485-4912009-04-18RePEc:oup:biomet

article Generalised minimum aberration is a recently-established design criterion for the whole class of orthogonal arrays and fractional factorial designs. The criterion is, as its name suggests, a generalisation of minimum aberration for regular designs and of minimum G-sub-2-aberration for twolevel designs. The aim of the criterion is to find designs which minimise in a certain sense the aliasing between main effects and interactions. In this paper, theoretical results are developed for finding symmetrical orthogonal arrays with generalised minimum aberration for more than two factor levels. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 485 491 http://hdl.handle.net/10.1093/biomet/92.2.485 text/html Access to full text is restricted to subscribers. Neil A. Butler

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:425-4382009-04-18RePEc:oup:biomet

article We employ second-order likelihood asymptotics to investigate how ideal frequentist inferences depend on the probability model for the data through more than the likelihood function, referring to this as the effect of the reference set. There are two aspects of higherorder corrections to first-order likelihood methods, namely (i) that involving effects of fitting nuisance parameters and leading to the modified profile likelihood, and (ii) another part pertaining to limitation in adjusted information. Generally, each of these involves a first-order adjustment depending on the reference set. However, we show that, for some important settings, likelihood-irrelevant model specifications have a second-order effect on both of these adjustments; this result includes specification of the censoring model for survival data. On the other hand, for sequential experiments the likelihood-irrelevant specification of the stopping rule has a second-order effect on adjustment (i) but a firstorder effect on adjustment (ii). These matters raise the issue of what are 'ideal' frequentist inferences, since consideration of 'exact' frequentist inferences will not suffice. We indicate that to second order ideal frequentist inferences may be based on the distribution of the ordinary likelihood ratio statistic, without commonly considered adjustments thereto. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 425 438 http://hdl.handle.net/10.1093/biomet/93.2.425 text/html Access to full text is restricted to subscribers. Donald A. Pierce Ruggero Bellio

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:943-9542009-04-18RePEc:oup:biomet

article When the estimating function for a vector of parameters is not smooth, it is often rather difficult, if not impossible, to obtain a consistent estimator by solving the corresponding estimating equation using standard numerical techniques. In this paper, we propose a simple inference procedure via the importance sampling technique, which provides a consistent root of the estimating equation and also an approximation to its distribution without solving any equations or involving nonparametric function estimates. The new proposal is illustrated and evaluated via two extensive examples with real and simulated datasets. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 943 954 http://hdl.handle.net/10.1093/biomet/91.4.943 text/html Access to full text is restricted to subscribers. L. Tian J. Liu Y. Zhao L. J. Wei

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:841-8602009-04-18RePEc:oup:biomet

article We propose a new class of models for making inference about the mean of a vector of repeated outcomes when the outcome vector is incompletely observed in some study units and missingness is nonmonotone. Each model in our class is indexed by a set of unidentified selection-bias functions which quantify the residual association of the outcome at each occasion t and the probability that this outcome is missing after adjusting for variables observed prior to time t and for the past nonresponse pattern. In particular, selection-bias functions equal to zero encode the investigator's a priori belief that nonresponse of the next outcome does not depend on that outcome after adjusting for the observed past. We call this assumption sequential explainability. Since each model in our class is nonparametric, it fits the data perfectly well. As such, our models are ideal for conducting sensitivity analyses aimed at evaluating the impact that different degrees of departure from sequential explainability have on inference about the marginal means of interest. Although the marginal means are identified under each of our models, their estimation is not feasible in practice because it requires the auxiliary estimation of conditional expectations and probabilities given high-dimensional variables. We henceforth discuss the estimation of the marginal means under each model in our class assuming, additionally, that at each occasion either one of the following two models holds: a parametric model for the conditional probability of nonresponse given current outcomes and past recorded data or a parametric model for the conditional mean of the outcome on the nonrespondents given the past recorded data. We call the resulting procedure 2-super-T-multiply robust as it protects at each of the T time points against misspecification of one of these two working models, although not against simultaneous misspecification of both. We extend our proposed class of models and estimators to incorporate data configurations which include baseline covariates and a parametric model for the conditional mean of the vector of repeated outcomes given the baseline covariates. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 841 860 http://hdl.handle.net/10.1093/biomet/asm070 application/pdf Access to full text is restricted to subscribers. Stijn Vansteelandt Andrea Rotnitzky James Robins

oai:RePEc:oup:biomet:v:94:y:2007:i:4:p:953-9642009-04-18RePEc:oup:biomet

article Existing jackknife variance estimators used with sample surveys can seriously overestimate the true variance under unistage stratified sampling without replacement with unequal probabilities. A novel jackknife variance estimator is proposed which is as numerically simple as existing jackknife variance estimators. Under certain regularity conditions, the proposed variance estimator is consistent under stratified sampling without replacement with unequal probabilities. The high entropy regularity condition necessary for consistency is shown to hold for the Rao--Sampford design. An empirical study of three unequal probability sampling designs supports our findings. Copyright 2007, Oxford University Press. 4 2007 94 Biometrika 953 964 http://hdl.handle.net/10.1093/biomet/asm072 application/pdf Access to full text is restricted to subscribers. Yves G. Berger

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:29-412009-04-18RePEc:oup:biomet

article The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 29 41 You-Gan Wang

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:735-7462009-04-18RePEc:oup:biomet

article A distribution is conditionally specified when its model constraints are expressed conditionally. For example, Besag's (1974) spatial model was specified conditioned on the neighbouring states, and pseudolikelihood is intended to approximate the likelihood using conditional likelihoods. There are three issues of interest: existence, uniqueness and computation of a joint distribution. In the literature, most results and proofs are for discrete probabilities; here we exclusively study distributions with continuous state space. We examine all three issues using the dependence functions derived from decomposition of the conditional densities. We show that certain dependence functions of the joint density are shared with its conditional densities. Therefore, two conditional densities involving the same set of variables are compatible if their overlapping dependence functions are identical. We prove that the joint density is unique when the set of dependence functions is both compatible and complete. In addition, a joint density, apart from a constant, can be computed from the dependence functions in closed form. Since all of the results are expressed in terms of dependence functions, we consider our approach to be dependence-based, whereas methods in the literature are generally density-based. Applications of the dependence-based formulation are discussed. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 735 746 http://hdl.handle.net/10.1093/biomet/asn029 application/pdf Access to full text is restricted to subscribers. Yuchung J. Wang Edward H. Ip

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:221-2272009-04-18RePEc:oup:biomet

article We derive some readily verifiable necessary and sufficient conditions for a multivariate non-Gaussian linear process to be time-reversible, under two sets of conditions on the contemporaneous dependence structure of the innovations. One set of conditions concerns the case of independent-component innovations, in which case a multivariate non-Gaussian linear process is time-reversible if and only if the coefficients consist of essentially asymmetric columns with column-specific origins of symmetry or symmetric pairs of columns with pair-specific origins of symmetry. On the other hand, for dependent-component innovations plus other regularity conditions, a multivariate non-Gaussian linear process is time-reversible if and only if the coefficients are essentially symmetric about some origin. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 221 227 http://hdl.handle.net/10.1093/biomet/93.1.221 text/html Access to full text is restricted to subscribers. Kung-Sik Chan Lop-Hing Ho Howell Tong

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:141-1512009-04-18RePEc:oup:biomet

article We specify some conditions for the identification of a multi-factor model with correlated residuals, uncorrelated factors and zero restrictions in the factor loadings. These conditions are derived from the results of Stanghellini (1997) and Vicard (2000) which deal with single-factor models with zero restrictions in the concentration matrix. Like these authors, we make use of the complementary graph of residuals and the conditions build on the role of odd cycles in this graph. However, in contrast to these authors, we consider the case where the conditional dependencies of the residuals are expressed in terms of a covariance matrix rather than its inverse, the concentration matrix. We first derive the corresponding condition for identification of single-factor models with structural zeros in the covariance matrix of the residuals. This is extended to the case where some factor loadings are constrained to be zero. We use these conditions to obtain a sufficient and a necessary condition for identification of multi-factor models. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 141 151 Michel Grzebyk

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:785-8062009-04-18RePEc:oup:biomet

article Extending the work of Dupuis (1995), we motivate a range of biologically plausible models for multiple-site capture-recapture and show how the original Gibbs sampling algorithm of Dupuis can be extended to obtain posterior model probabilities using reversible jump Markov chain Monte Carlo. This model selection procedure improves upon previous analyses in two distinct ways. First, Bayesian model averaging provides a robust parameter estimation technique which properly incorporates model uncertainty in the resulting intervals. Secondly, by discriminating among perhaps millions of competing models, we are able to discern fine structure within the data and thereby answer questions of primary biological importance. We demonstrate how reversible jump Markov chain Monte Carlo methods provide the only viable method for exploring model spaces of this size. We examine the lizard data discussed in Dupuis (1995) and show that most of the posterior mass is placed upon models not previously considered for these data. We discuss model discrimination and model averaging and focus upon the increased scientific understanding of the data obtained via the Bayesian model comparison procedure. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 785 806 R. King

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:845-8582009-04-18RePEc:oup:biomet

article In settings where the full probability model is not specified, consider a general estimating function g(&thgr;, &lgr;; y) that involves not only the parameters of interest, &thgr;, but also some nuisance parameters, &lgr;. We consider methods for reducing the effects on g of fitting nuisance parameters. We propose Cox--Reid-type adjustment to the profile estimating function, g(&thgr;, &lgr;ˆ-sub-&thgr;; y), that reduces its bias by two orders. Typically, only the first two moments of the response variable are needed to form the adjustment. Important applications of this method include the estimation of the pairwise association and main effects in stratified, clustered data and estimation of the main effects in a matched pair study. A brief simulation study shows that the proposed method considerably reduces the impact of the nuisance parameters. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 845 858 Molin Wang

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:1-162009-04-18RePEc:oup:biomet

article We have a statistic for assessing an observed data point relative to a statistical model but find that its distribution function depends on the parameter. To obtain the corresponding p-value, we require the minimally modified statistic that is ancillary; this process is called Studentization. We use recent likelihood theory to develop a maximal third-order ancillary; this gives immediately a candidate Studentized statistic. We show that the corresponding p-value is higher-order Un(0, 1), is equivalent to a repeated bootstrap version of the initial statistic and agrees with a special Bayesian modification of the original statistic. More importantly, the modified statistic and p-value are available by Markov chain Monte Carlo simulations and, in some cases, by higher-order approximation methods. Examples, including the Behrens--Fisher problem, are given to indicate the ease and flexibility of the approach. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 1 16 http://hdl.handle.net/10.1093/biomet/asm093 application/pdf Access to full text is restricted to subscribers. D.A.S. Fraser Judith Rousseau

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:365-3792009-04-18RePEc:oup:biomet

article We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to some nonstationary time series. The unobservable, nonstationary factors are identified by expanding the white noise space step by step, thereby solving a high-dimensional optimization problem by several low-dimensional sub-problems. Asymptotic properties of the estimation are investigated. The proposed methodology is illustrated with both simulated and real datasets. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 365 379 http://hdl.handle.net/10.1093/biomet/asn009 application/pdf Access to full text is restricted to subscribers. Jiazhu Pan Qiwei Yao

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:478-4812009-04-18RePEc:oup:biomet

article We propose a new archimedean copula model for bivariate survival data that is motivated by Dabrowska's (1988) measure of association. The model can represent negatively correlated or moderately positively correlated data but not highly positively correlated data. Local and global measures of association are calculated. A generalisation is presented. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 478 481 David Oakes

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:831-8452009-04-18RePEc:oup:biomet

article We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function <inline-formula><inline-graphic xlink:href="asn045ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of <inline-formula><inline-graphic xlink:href="asn045ilm2.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> and develop a test statistic based on them. Our test statistic has a limiting standard normal distribution, so that the test can be performed by simply comparing the test statistic with readily available critical values. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 831 845 http://hdl.handle.net/10.1093/biomet/asn045 application/pdf Access to full text is restricted to subscribers. Yongtao Guan

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:587-6002009-04-18RePEc:oup:biomet

article We present robust estimators for the mean and the principal components of a stochastic process in <inline-formula><inline-graphic xlink:href="asn031ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula>. Robustness and asymptotic properties of the estimators are studied theoretically, by simulation and by example. It is shown that the proposed estimators are generally more robust to outliers than the commonly used sample mean and principal components, although their properties depend on the spacings of the eigenvalues of the covariance function. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 587 600 http://hdl.handle.net/10.1093/biomet/asn031 application/pdf Access to full text is restricted to subscribers. Daniel Gervini

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:585-5962009-04-18RePEc:oup:biomet

article Estimation of a receiver operating characteristic, ROC, curve is usually based either on a fully parametric model such as a normal model or on a fully nonparametric model. In this paper, we explore a semiparametric approach by assuming a density ratio model for disease and disease-free densities. This model has a natural connection with the logistic regression model. The proposed semiparametric approach is more robust than a fully parametric approach and is more efficient than a fully nonparametric approach. Two real examples demonstrate that the ROC curve estimated by our semiparametric method is much smoother than that estimated by the nonparametric method. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 585 596 Jing Qin

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:187-2042009-04-18RePEc:oup:biomet

article We consider the problem of estimating the population total in two-stage cluster sampling when cluster sizes are known only for the sampled clusters, making use of a population model arising from a variance component model. The problem can be considered as one of predicting the unobserved part Z of the total, and the concept of predictive likelihood is studied. Prediction intervals and a predictor for the population total are derived for the normal case, based on predictive likelihood. For a more general distribution-free model, by application of an analysis of variance approach instead of maximum likelihood for parameter estimation, the predictor obtained from the predictive likelihood is shown to be approximately uniformly optimal for large sample size and large number of clusters, in the sense of uniformly minimizing the mean-squared error in a partially linear class of model-unbiased predictors. Three prediction intervals for Z based on three similar predictive likelihoods are studied. For a small number n₀ of sampled clusters, they differ significantly, but for large n₀, the three intervals are practically identical. Model-based and design-based coverage properties of the prediction intervals are studied based on a comprehensive simulation study. The simulation study indicates that for large sample sizes, the coverage measures achieve approximately the nominal level 1 - α and are slightly less than 1 - α for moderately large sample sizes. For small sample sizes, the coverage measures are about 1 - 2α, being raised to 1 - α for a modified interval based on the <inline-formula><inline-graphic xlink:href="asm098ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> distribution. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 187 204 http://hdl.handle.net/10.1093/biomet/asm098 application/pdf Access to full text is restricted to subscribers. Jan F. Bjørnstad Elinor Ytterstad

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:821-8302009-04-18RePEc:oup:biomet

article We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. For the special case of a one-dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved by some existing methods. We conduct extensive simulations to evaluate finite-sample performance of our method and compare it with existing methods. Our method can be extended to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered designed points. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 821 830 http://hdl.handle.net/10.1093/biomet/92.4.821 text/html Access to full text is restricted to subscribers. Tiejun Tong Yuedong Wang

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:929-9412009-04-18RePEc:oup:biomet

article This paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters. In a statistical model with unknown nuisance parameters, the efficiency of an estimator of a parameter usually increases when the nuisance parameters are known. However the opposite phenomenon can sometimes occur. In this paper, we elucidate the occurrence of this paradox by examining estimating functions. In particular, we focus on the projected estimating function, which is defined by the projection of the score function on to a given estimating function. A sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters. In addition, a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 929 941 http://hdl.handle.net/10.1093/biomet/91.4.929 text/html Access to full text is restricted to subscribers. Masayuki Henmi Shinto Eguchi

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:317-3352009-04-18RePEc:oup:biomet

article A centred Gaussian model that is Markov with respect to an undirected graph G is characterised by the parameter set of its precision matrices which is the cone M-super-&plus;(G) of positive definite matrices with entries corresponding to the missing edges of G constrained to be equal to zero. In a Bayesian framework, the conjugate family for the precision parameter is the distribution with Wishart density with respect to the Lebesgue measure restricted to M-super-&plus;(G). We call this distribution the G-Wishart. When G is nondecomposable, the normalising constant of the G-Wishart cannot be computed in closed form. In this paper, we give a simple Monte Carlo method for computing this normalising constant. The main feature of our method is that the sampling distribution is exact and consists of a product of independent univariate standard normal and chi-squared distributions that can be read off the graph G. Computing this normalising constant is necessary for obtaining the posterior distribution of G or the marginal likelihood of the corresponding graphical Gaussian model. Our method also gives a way of sampling from the posterior distribution of the precision matrix. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 317 335 http://hdl.handle.net/10.1093/biomet/92.2.317 text/html Access to full text is restricted to subscribers. Aliye Atay-Kayis Helène Massam

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:691-7012009-04-18RePEc:oup:biomet

article The recent paper by Peng & Yao (2003) gave an interesting extension of least absolute deviation estimation to generalised autoregressive conditional heteroscedasticity, GARCH, time series models. The asymptotic distributions of absolute residual autocorrelations and squared residual autocorrelations from the GARCH model estimated by the least absolute deviation method are derived in this paper. These results lead to two useful diagnostic tools which can be used to check whether or not a GARCH model fitted by using the least absolute deviation method is adequate. Some simulation experiments give further support to the asymptotic theory and a real data example is also reported. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 691 701 http://hdl.handle.net/10.1093/biomet/92.3.691 text/html Access to full text is restricted to subscribers. Guodong Li Wai Keung Li

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:183-1962009-04-18RePEc:oup:biomet

article In this paper based on a basic area level model we obtain second-order accurate approximations to the mean squared error of model-based small area estimators, using the Fay & Herriot (1979) iterative method of estimating the model variance based on weighted residual sum of squares. We also obtain mean squared error estimators unbiased to second order. Based on simulations, we compare the finite-sample performance of our mean squared error estimators with those based on method-of-moments, maximum likelihood and residual maximum likelihood estimators of the model variance. Our results suggest that the Fay--Herriot method performs better, in terms of relative bias of mean squared error estimators, than the other methods across different combinations of number of areas, pattern of sampling variances and distribution of small area effects. We also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second-order unbiased for the mean squared error. The posterior variance based on such a prior possesses both Bayesian and frequentist interpretations. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 183 196 http://hdl.handle.net/10.1093/biomet/92.1.183 text/html Access to full text is restricted to subscribers. Gauri Sankar Datta J. N. K. Rao David Daniel Smith

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:939-9462009-04-18RePEc:oup:biomet

article Monitoring the t-tests for individual regression coefficients in 'forward' search fails to identify the importance of observations to the significance of the individual regressors. This failure is due to the ordering of the data by the search. We introduce an added-variable test which has the desired properties since the projection leading to residuals destroys the effect of the ordering. An example illustrates the effect of several masked outliers on model selection. Comments are given on the related test for response transformations. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 939 946 Anthony C. Atkinson

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:331-3432009-04-18RePEc:oup:biomet

article A general class of semiparametric transformation cure models is studied for the analysis of survival data with long-term survivors. It combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. Included as special cases are the proportional hazards cure model (Farewell, 1982&semi; Kuk & Chen, 1992&semi; Sy & Taylor, 2000&semi; Peng & Dear, 2000) and the proportional odds cure model. Generalised estimating equations are proposed for parameter estimation. It is shown that the resulting estimators are asymptotically normal, with variance-covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. Simulation studies show that the proposed approach is appropriate for practical use. An application to data from a breast cancer study is given to illustrate the methodology. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 331 343 Wenbin Lu

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:779-7862009-04-18RePEc:oup:biomet

article The covariance between two variables in a multivariate Gaussian distribution is decomposed into a sum of path weights for all paths connecting the two variables in an undirected independence graph. These weights are useful in determining which variables are important in mediating correlation between the two path endpoints. The decomposition arises in undirected Gaussian graphical models and does not require or involve any assumptions of causality. This covariance decomposition is derived using basic linear algebra. The decomposition is feasible for very large numbers of variables if the corresponding precision matrix is sparse, a circumstance that arises in examples such as gene expression studies in functional genomics. Additional computational efficiences are possible when the undirected graph is derived from an acyclic directed graph. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 779 786 http://hdl.handle.net/10.1093/biomet/92.4.779 text/html Access to full text is restricted to subscribers. Beatrix Jones Mike West

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:59-742009-04-18RePEc:oup:biomet

article This paper proposes a classical weighted least squares type of local polynomial smoothing for the analysis of clustered data, with the key idea of using generalised inverses of correlation matrices. The estimator has a simple closed-form expression. Simplicity is achieved also for nonparametric generalised linear models with arbitrary link function via a transformation. Our approach can be characterised by 'local observations with local variances', which yields intuitively correct results in the sense that correct/incorrect specification of within-cluster correlation has respective positive/negative effects. The approach is a natural extension of classical local polynomial smoothing. Consequently, existing theory can be largely carried over and important issues such as bandwidth selection can be tackled in the classical fashion. Moreover, the approach can handle various types of covariate, such as cluster-level, subject-level or partially cluster-level. Numerical studies support the theoretical results. The method is illustrated with a real example on luteinising hormone levels in cows. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 59 74 http://hdl.handle.net/10.1093/biomet/92.1.59 text/html Access to full text is restricted to subscribers. Kani Chen Zhezhen Jin

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:49-612009-04-18RePEc:oup:biomet

article Sufficient-component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of sufficient causes, synergism and sufficient cause interactions. Doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of sufficient cause interactions. The conditions are novel in that, unlike other conditions in the literature, they make no assumption about monotonicity. The conditions can also be generalized and the conditions for three-way sufficient cause interactions are given explicitly. The statistical tests derived for sufficient cause interactions are compared with and contrasted to interaction terms in standard statistical models. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 49 61 http://hdl.handle.net/10.1093/biomet/asm090 application/pdf Access to full text is restricted to subscribers. Tyler J. Vanderweele James M. Robins

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:49-602009-04-18RePEc:oup:biomet

article We consider the problem of testing a statistical hypothesis where the scientifically meaningful test statistic is a function of latent variables. In particular, we consider detection of genetic linkage, where the latent variables are patterns of inheritance at specific genome locations. Introduced by Geyer & Meeden (2005), fuzzy p-values are random variables, described by their probability distributions, that are interpreted as p-values. For latent variable problems, we introduce the notion of a fuzzy p-value as having the conditional distribution of the latent p-value given the observed data, where the latent p-value is the random variable that would be the p-value if the latent variables were observed.The fuzzy p-value provides an exact test using two sets of simulations of the latent variables under the null hypothesis, one unconditional and the other conditional on the observed data. It provides not only an expression of the strength of the evidence against the null hypothesis but also an expression of the uncertainty in that expression owing to lack of knowledge of the latent variables. We illustrate these features with an example of simulated data mimicking a real example of the detection of genetic linkage. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 49 60 http://hdl.handle.net/10.1093/biomet/asm001 application/pdf Access to full text is restricted to subscribers. Elizabeth A. Thompson Charles J. Geyer

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:113-1252009-04-18RePEc:oup:biomet

article We use a reproducing kernel Hilbert space representation to derive the smoothing spline solution when the smoothness penalty is a function λ(t) of the design space t, thereby allowing the model to adapt to various degrees of smoothness in the structure of the data. We propose a convenient form for the smoothness penalty function and discuss computational algorithms for automatic curve fitting using a generalised crossvalidation measure. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 113 125 http://hdl.handle.net/10.1093/biomet/93.1.113 text/html Access to full text is restricted to subscribers. Alexandre Pintore Paul Speckman Chris C. Holmes

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:861-8752009-04-18RePEc:oup:biomet

article The common principal components model for several groups of multivariate observations assumes equal principal axes but different variances along these axes among the groups. Influence functions for plug-in and projection-pursuit estimates under a common principal component model are obtained. Asymptotic variances are derived from them. Outlier detection is possible using partial influence functions. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 861 875 Graciela Boente

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:491-5122009-04-18RePEc:oup:biomet

article We consider the problem of comparing parametric models using a Bayesian approach. A new method of developing prior distributions for the model parameters is presented, called the expected-posterior prior approach. The idea is to define the priors for all models from a common underlying predictive distribution, in such a way that the resulting priors are amenable to modern Markov chain Monte Carlo computational techniques. The approach has subjective Bayesian and default Bayesian implementations, and overcomes the most significant impediment to Bayesian model selection, that of ensuring that prior distributions for the various models are appropriately compatible. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 491 512 Jose M. Perez

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:987-9942009-04-18RePEc:oup:biomet

article In this paper, the difference between two correlated t variables is divided by a function of their sample correlation and the distribution of the resulting quantity is examined. Functions of the sample correlation are found for which this quantity is approximately pivotal and has a t distribution, asymptotically. Simulations show that the asymptotic results hold well for small sample sizes. The results yield a useful test for comparing the difference in standardised scores of an individual with those of a group of controls. The test assumes that sampling is from a bivariate normal distribution and robustness of the test to departure from normality is examined. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 987 994 http://hdl.handle.net/10.1093/biomet/91.4.987 text/html Access to full text is restricted to subscribers. Paul H. Garthwaite John R. Crawford

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:385-3972009-04-18RePEc:oup:biomet

article The Nordstrom--Robinson code is a well-known nonlinear code in coding theory. This paper explores the statistical properties of this nonlinear code. Many nonregular designs with 32, 64, 128 and 256 runs and 7--16 factors are derived from it. It is shown that these nonregular designs are better than regular designs of the same size in terms of resolution, aberration and projectivity. Furthermore, many of these nonregular designs are shown to have generalised minimum aberration among all possible designs. Seven orthogonal arrays are shown to have unique word-length pattern and four of them are shown to be unique up to isomorphism. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 385 397 http://hdl.handle.net/10.1093/biomet/92.2.385 text/html Access to full text is restricted to subscribers. Hongquan Xu

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:221-2322009-04-18RePEc:oup:biomet

article Most research on the study of associations among paired failure times has either assumed time invariance or been based on complex measures or estimators. Little has accommodated competing risks. This paper targets the conditional cause-specific hazard ratio, henceforth called the cause-specific cross ratio, a recent modification of the conditional hazard ratio designed to accommodate competing risks data. Estimation is accomplished by an intuitive, nonparametric method that localizes Kendall's tau. Time variance is accommodated through a partitioning of space into 'bins' between which the strength of association may differ. Inferential procedures are developed, small-sample performance is evaluated, and the methods are applied to the investigation of familial association in dementia onset. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 221 232 http://hdl.handle.net/10.1093/biomet/asm091 application/pdf Access to full text is restricted to subscribers. Karen Bandeen-Roche Jing Ning

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:91-1032009-04-18RePEc:oup:biomet

article Penalised-spline-based additive models allow a simple mixed model representation where the variance components control departures from linear models. The smoothing parameter is the ratio of the random-coefficient and error variances and tests for linear regression reduce to tests for zero random-coefficient variances. We propose exactlikelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines. Their spectral decompositions are used as the basis of fast simulation algorithms. We derive the asymptotic local power properties of the tests under weak conditions. In particular we characterise the local alternatives that are detected with asymptotic probability one. Confidence intervals for the smoothing parameter are obtained by inverting the tests for a fixed smoothing parameter versus a general alternative. We discuss F and R tests and show that ignoring the variability in the smoothing parameter estimator can have a dramatic effect on their null distributions. The powers of several known tests are investigated and a small set of tests with good power properties is identified. The restricted likelihood ratio test is among the best in terms of power. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 91 103 http://hdl.handle.net/10.1093/biomet/92.1.91 text/html Access to full text is restricted to subscribers. Ciprian Crainiceanu David Ruppert Gerda Claeskens M. P. Wand

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:199-2162009-04-18RePEc:oup:biomet

article We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm has guaranteed convergence properties. Dropping the assumption of multivariate normality, we show how to estimate the covariance matrix in an empirical likelihood approach. These approaches are then compared via simulation and on an example of gene expression. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 199 216 http://hdl.handle.net/10.1093/biomet/asm007 application/pdf Access to full text is restricted to subscribers. Sanjay Chaudhuri Mathias Drton Thomas S. Richardson

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:393-4102009-04-18RePEc:oup:biomet

article Prepivoting by conventional bootstrap iteration is known to yield a progressively more accurate pivot in certain problems, and has important application in the construction of confidence limits and estimation of null distributions. We investigate the theoretical effects of weighted bootstrap iteration on prepivoting and show that each weighted bootstrap iteration, with weights chosen carefully but empirically, is asymptotically equivalent to two consecutive conventional bootstrap iterations. In terms of reducing the order of error, prepivoting can therefore be carried out much more efficiently if based on weighted bootstrap iterations. This is shown for a variety of problem settings, including the smooth function model, M-estimation and the regression context. A numerical illustration is provided, demonstrating the potential practical usefulness of weighted prepivoting. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 393 410 Stephen M. S. Lee

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:695-7072009-04-18RePEc:oup:biomet

article In two-stage adaptive treatment strategies, patients receive an induction treatment followed by a maintenance therapy, given that the patient responded to the induction treatment they received. To test for a difference in the effects of different induction and maintenance treatment combinations, a modified supremum weighted log-rank test is proposed. The test is applied to a dataset from a two-stage randomized trial and the results are compared to those obtained using a standard weighted log-rank test. A sample-size formula is proposed based on the limiting distribution of the supremum weighted log-rank statistic. The sample-size formula reduces to Eng and Kosorok's sample-size formula for a two-sample supremum log-rank test when there is no second randomization. Monte Carlo studies show that the proposed test provides sample sizes that are close to those obtained by standard weighted log-rank test under a proportional hazards alternative. However, the proposed test is more powerful than the standard weighted log-rank test under non-proportional hazards alternatives. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 695 707 http://hdl.handle.net/10.1093/biomet/asn025 application/pdf Access to full text is restricted to subscribers. Wentao Feng Abdus S. Wahed

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:95-1062009-04-18RePEc:oup:biomet

article Motivated by a Bayesian framework, we propose a new minimum aberration-type criterion for designing experiments with two- and four-level factors. The Bayesian approach helps in overcoming the ad hoc nature of effect ordering in the existing minimum aberration-type criteria. The approach is also capable of distinguishing between qualitative and quantitative factors. Numerous examples are given to demonstrate its advantages. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 95 106 http://hdl.handle.net/10.1093/biomet/asn062 application/pdf Access to full text is restricted to subscribers. V. Roshan Joseph Mingyao AI C. F. Jeff Wu

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:175-1862009-04-18RePEc:oup:biomet

article One of the attractions of crossvalidation, as a tool for smoothing-parameter choice, is its applicability to a wide variety of estimator types and contexts. However, its detractors comment adversely on the relatively high variance of crossvalidatory smoothing parameters, noting that this compromises the performance of the estimators in which those parameters are used. We show that the variability can be reduced simply, significantly and reliably by employing bootstrap aggregation or bagging. We establish that in theory, when bagging is implemented using an adaptively chosen resample size, the variability of crossvalidation can be reduced by an order of magnitude. However, it is arguably more attractive to use a simpler approach, based for example on half-sample bagging, which can reduce variability by approximately 50%. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 175 186 http://hdl.handle.net/10.1093/biomet/asn068 application/pdf Access to full text is restricted to subscribers. Peter Hall Andrew P. Robinson

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:881-8902009-04-18RePEc:oup:biomet

article This paper compares the second-order power properties of a broad class of nonparametric likelihood tests recently introduced by Baggerly (1998) as a generalisation of Owen's (1988) empirical likelihood. It is shown that in a multi-parameter setting identity of power up to first order does not imply identity up to second order unless one considers the average power criterion. It is also shown that the empirical likelihood ratio enjoys an optimality property in terms of local maximinity. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 881 890 Francesco Bravo

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:831-8442009-04-18RePEc:oup:biomet

article Estimation of an unstructured covariance matrix is difficult because of its positive-definiteness constraint. This obstacle is removed by regressing each variable on its predecessors, so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying-coefficient and varying-order regression models. Our framework is similar to the use of increasing-order autoregressive models in approximating the covariance matrix or the spectrum of a stationary time series. As an illustration, we adopt Fan & Zhang's (2000) two-step estimation of functional linear models and propose nonparametric estimators of covariance matrices which are guaranteed to be positive definite. For parsimony a suitable order for the sequence of (auto)regression models is found using penalised likelihood criteria like AIC and BIC. Some asymptotic results for the local polynomial estimators of components of a covariance matrix are established. Two longitudinal datasets are analysed to illustrate the methodology. A simulation study reveals the advantage of the nonparametric covariance estimator over the sample covariance matrix for large covariance matrices. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 831 844 Wei Biao Wu

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:709-7192009-04-18RePEc:oup:biomet

article Benjamini and Hochberg's method for controlling the false discovery rate is applied to the problem of testing infinitely many contrasts in linear models. Exact, easily calculated critical values are derived, defining a new multiple comparisons method for testing contrasts in linear models. The method is adaptive, depending on the data through the F-statistic, like the Waller--Duncan Bayesian multiple comparisons method. Comparisons with Scheffé's method are given, and the method is extended to the simultaneous confidence intervals of Benjamini and Yekutieli. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 709 719 http://hdl.handle.net/10.1093/biomet/asn033 application/pdf Access to full text is restricted to subscribers. Peter H. Westfall

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:533-5492009-04-18RePEc:oup:biomet

article It is well known, at least through many examples, that when there are many nuisance parameters modified profile likelihoods often perform much better than the profile likelihood. Ordinary asymptotics almost totally fail to deal with this issue. For this reason, we study asymptotic properties of the profile and modified profile likelihoods in models for stratified data in a two-index asymptotics setting. This means that both the sample size of the strata, m, and the dimension of the nuisance parameter, q, may increase to infinity. It is shown that in this asymptotic setting modified profile likelihoods give improvements, with respect to the profile likelihood, in terms of consistency of estimators and of asymptotic distributional properties. In particular, the modified profile likelihood based statistics have the usual asymptotic distribution, provided that 1&sol;m &equals; o(q-super- - 1&sol;3), while the analogous condition for the profile likelihood is 1&sol;m &equals; o(q-super- - 1). Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 533 549 N. Sartori

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:23-402009-04-18RePEc:oup:biomet

article The combination of graphical models and reference analysis represents a powerful tool for Bayesian inference in highly multivariate settings. It is typically difficult to derive reference priors in complex problems. In this paper we present a suitable mixed parameterisation for a discrete decomposable graphical model and derive the corresponding reference prior. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 23 40 http://hdl.handle.net/10.1093/biomet/93.1.23 text/html Access to full text is restricted to subscribers. Guido Consonni Valentina Leucari

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:499-5032009-04-18RePEc:oup:biomet

article We consider a very general class of empirical discrepancy statistics that includes the Cressie--Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order asymptotics for expected lengths of associated confidence intervals are investigated. An explicit formula is worked out and its use for comparative purposes is discussed. It is seen that the empirical likelihood ratio statistic, which enjoys interesting second-order power properties, loses much of its edge under the present criterion. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 499 503 http://hdl.handle.net/10.1093/biomet/92.2.499 text/html Access to full text is restricted to subscribers. Kai-tai Fang Rahul Mukerjee

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:635-6512009-04-18RePEc:oup:biomet

article Often there is substantial uncertainty in the selection of confounders when estimating the association between an exposure and health. We define this type of uncertainty as `adjustment uncertainty'. We propose a general statistical framework for handling adjustment uncertainty in exposure effect estimation for a large number of confounders, we describe a specific implementation, and we develop associated visualization tools. Theoretical results and simulation studies show that the proposed method provides consistent estimators of the exposure effect and its variance. We also show that, when the goal is to estimate an exposure effect accounting for adjustment uncertainty, Bayesian model averaging with posterior model probabilities approximated using information criteria can fail to estimate the exposure effect and can over- or underestimate its variance. We compare our approach to Bayesian model averaging using time series data on levels of fine particulate matter and mortality. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 635 651 http://hdl.handle.net/10.1093/biomet/asn015 application/pdf Access to full text is restricted to subscribers. Ciprian M. Crainiceanu Francesca Dominici Giovanni Parmigiani

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:635-6482009-04-18RePEc:oup:biomet

article We derive the limiting distribution of the partial likelihood ratio under general conditions. The multiplicative hazards models being fitted may be nonnested and misspecified. The true model is not assumed to contain either model under consideration. The null hypothesis is that the models are equidistant in Kullback--Leibler metric applied to the rank likelihood. The statistic is consistent for the model which is closer to the truth. Its distribution depends on the unknown data-generating mechanism. A sequential testing procedure is proposed for nonnested comparisons which is valid regardless of the true model. This involves a novel statistic for the equality of the fitted models which is separate from the partial likelihood. The methodology has important applications in model assessment. Simulations and a real example demonstrate its utility in selecting the functional forms of covariates and relative risks. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 635 648 J. P. Fine

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:51-652009-04-18RePEc:oup:biomet

article We introduce a method for constructing a rich class of designs that are suitable for use in computer experiments. The designs include Latin hypercube designs and two-level fractional factorial designs as special cases and fill the vast vacuum between these two familiar classes of designs. The basic construction method is simple, building a series of larger designs based on a given small design. If the base design is orthogonal, the resulting designs are orthogonal; likewise, if the base design is nearly orthogonal, the resulting designs are nearly orthogonal. We present two generalizations of our basic construction method. The first generalization improves the projection properties of the basic method; the second generalization gives rise to designs that have smaller correlations. Sample constructions are presented and properties of these designs are discussed. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 51 65 http://hdl.handle.net/10.1093/biomet/asn057 application/pdf Access to full text is restricted to subscribers. Derek Bingham Randy R. Sitter Boxin Tang

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:539-5522009-04-18RePEc:oup:biomet

article Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes in order to explore consistently a sequence of multiple distributions of interest. We show that such methods can also offer an efficient estimation tool in 'static' set-ups, in which case &pgr;(&thgr; | y-sub-1, …, y-sub-N) (n < N) is the only posterior distribution of interest but the preliminary exploration of partial posteriors &pgr;(&thgr; | y-sub-1, …, y-sub-n) makes it possible to save computing time. A complete algorithm is proposed for independent or Markov models. Our method is shown to challenge other common estimation procedures in terms of robustness and execution time, especially when the sample size is important. Two classes of examples, mixture models and discrete generalised linear models, are discussed and illustrated by numerical results. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 539 552 Nicolas Chopin

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:119-1322009-04-18RePEc:oup:biomet

article We investigate data tapering in two formulations of empirical likelihood for time series. One empirical likelihood is formed from tapered data blocks in the time domain and a second is based on the tapered periodogram in the frequency domain. Limiting distributions are provided for both empirical likelihood versions under tapering. Theoretical and simulation evidence indicates that a data taper improves the coverage accuracy of empirical likelihood confidence intervals for time series parameters, such as means and correlations. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 119 132 http://hdl.handle.net/10.1093/biomet/asn071 application/pdf Access to full text is restricted to subscribers. Daniel J. Nordman

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:303-3132009-04-18RePEc:oup:biomet

article In the statistical literature, life expectancy is usually characterised by the mean residual life function. Regression models are thus needed to study the association between the mean residual life functions and their covariates. In this paper, we consider a linear mean residual life model and develop inference procedures in the presence of potential censoring. The new model and inference procedures are applied to the Stanford heart transplant data. Semiparametric efficiency calculations and information bounds are also considered. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 303 313 http://hdl.handle.net/10.1093/biomet/93.2.303 text/html Access to full text is restricted to subscribers. Y. Q. Chen S. Cheng

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:653-6662009-04-18RePEc:oup:biomet

article We propose a generalization of the varying coefficient model for longitudinal data to cases where not only current but also recent past values of the predictor process affect current response. More precisely, the targeted regression coefficient functions of the proposed model have sliding window supports around current time t. A variant of a recently proposed two-step estimation method for varying coefficient models is proposed for estimation in the context of these generalized varying coefficient models, and is found to lead to improvements, especially for the case of additive measurement errors in both response and predictors. The proposed methodology for estimation and inference is also applicable for the case of additive measurement error in the common versions of varying coefficient models that relate only current observations of predictor and response processes to each other. Asymptotic distributions of the proposed estimators are derived, and the model is applied to the problem of predicting protein concentrations in a longitudinal study. Simulation studies demonstrate the efficacy of the proposed estimation procedure. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 653 666 http://hdl.handle.net/10.1093/biomet/asn006 application/pdf Access to full text is restricted to subscribers. Damla &Scedil;entürk Hans-Georg Müller

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:893-9042009-04-18RePEc:oup:biomet

article When fitting a linear regression model to data, aliasing can adversely affect the estimates of the model coefficients and the decision of whether or not a term is significant. Optimal experimental designs give efficient estimators assuming that the true form of the model is known, while robust experimental designs guard against inaccurate estimates caused by model misspecification. Although it is rare for a single design to be both maximally efficient and robust, it is shown here that uniform designs limit the effects of aliasing to yield reasonable efficiency and robustness together. Aberration and resolution measure how well fractional factorial designs guard against the effects of aliasing. Here it is shown that the definitions of aberration and resolution may be generalised to other types of design using the discrepancy. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 893 904 Fred J. Hickernell

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:1-212009-04-18RePEc:oup:biomet

article Methods have been proposed for redesigning a clinical trial at an interim stage in order to increase power. In order to preserve the type I error rate, methods for unplanned design-change have to be defined in terms of nonsufficient statistics, and this calls into question their efficiency and the credibility of conclusions reached. We evaluate schemes for adaptive redesign, extending the theoretical arguments for use of sufficient statistics of Tsiatis & Mehta (2003) and assessing the possible benefits of preplanned adaptive designs by numerical computation of optimal tests; these optimal adaptive designs are concrete examples of optimal sequentially planned sequential tests proposed by Schmitz (1993). We conclude that the flexibility of unplanned adaptive designs comes at a price and we recommend that the appropriate power for a study should be determined as thoroughly as possible at the outset. Then, standard error-spending tests, possibly with unevenly spaced analyses, provide efficient designs, but it is still possible to fall back on flexible methods for redesign should study objective change unexpectedly once the trial is under way. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 1 21 http://hdl.handle.net/10.1093/biomet/93.1.1 text/html Access to full text is restricted to subscribers. Christopher Jennison Bruce W. Turnbull

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:877-8912009-04-18RePEc:oup:biomet

article Generalised incomplete (m x n)&sol;k Trojan designs for m replicates of nk treatments based on sets of k cyclic generators are discussed. Normal equations for plots-within-columns, plots-within-blocks and blocks-within-columns treatment effects are developed. The nk treatments are divided into k subsets each of size n and the conditional plots-within-blocks and blocks-within-columns information matrix for each subset is defined. Efficient conditional treatment estimates are discussed and efficient generators for the various strata are discussed. Balanced (m x n)&sol;k incomplete Trojan designs based on Youden generators are constructed and designs based on multiples of a single generator are discussed. Some ideas for constructing efficient general (m x n)&sol;2 designs are outlined and some advantages of generalised incomplete Trojan designs are discussed. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 877 891 R. N. Edmondson

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:253-2562009-04-18RePEc:oup:biomet

article One-sided confidence intervals and overall p-values for group-sequential designs are typically based on a sample space ordering which determines both the overall p-value and the corresponding confidence bound. Accordingly, the strength of evidence against the null hypothesis is consistently measured by both quantities such that the order of the p-values of two distinct sample points is consistent with the order of the respective confidence bounds. An exception is the commonly used repeated p-values and repeated confidence intervals. We show that they are not ordering-consistent in the above sense and propose an alternative repeated p-value which is ordering-consistent and has the monitoring property of the classical repeated p-value in being valid even when deviating from the prefixed stopping rule. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 253 256 http://hdl.handle.net/10.1093/biomet/asm080 application/pdf Access to full text is restricted to subscribers. Martin Posch Gernot Wassmer Werner Brannath

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:647-6662009-04-18RePEc:oup:biomet

article This paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process. The model is a transparent extension of the accelerated failure time model for univariate survival data. Estimation of the regression parameter is motivated by semiparametric efficiency considerations, extending the class of weighted log-rank estimating functions originally proposed in Prentice (1978) and subsequently studied in detail by Tsiatis (1990) and Ritov (1990). A novel rank-based one-step estimator for the regression parameter is proposed. An Aalen-type estimator for the baseline intensity function is obtained. Asymptotics are handled with empirical process methods, and finite sample properties are studied via simulation. Finally, the new model is applied to the bladder tumour data of Byar (1980). Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 647 666 http://hdl.handle.net/10.1093/biomet/92.3.647 text/html Access to full text is restricted to subscribers. Robert L. Strawderman

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:149-1672009-04-18RePEc:oup:biomet

article Large margin classifiers have proven to be effective in delivering high predictive accuracy, particularly those focusing on the decision boundaries and bypassing the requirement of estimating the class probability given input for discrimination. As a result, these classifiers may not directly yield an estimated class probability, which is of interest itself. To overcome this difficulty, this article proposes a novel method for estimating the class probability through sequential classifications, by using features of interval estimation of large-margin classifiers. The method uses sequential classifications to bracket the class probability to yield an estimate up to the desired level of accuracy. The method is implemented for support vector machines and ψ-learning, in addition to an estimated Kullback--Leibler loss for tuning. A solution path of the method is derived for support vector machines to reduce further its computational cost. Theoretical and numerical analyses indicate that the method is highly competitive against alternatives, especially when the dimension of the input greatly exceeds the sample size. Finally, an application to leukaemia data is described. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 149 167 http://hdl.handle.net/10.1093/biomet/asm077 application/pdf Access to full text is restricted to subscribers. Junhui Wang Xiaotong Shen Yufeng Liu

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:229-2362009-04-18RePEc:oup:biomet

article Suppose that independent observations are drawn from multiple distributions, each of which is a mixture of two component distributions such that their log density ratio satisfies a linear model with a slope parameter and an intercept parameter. Inference for such models has been studied using empirical likelihood, and mixed results have been obtained. The profile empirical likelihood of the slope and intercept has an irregularity at the null hypothesis so that the two component distributions are equal. We derive a profile empirical likelihood and maximum likelihood estimator of the slope alone, and obtain the usual asymptotic properties for the estimator and the likelihood ratio statistic regardless of the null. Furthermore, we show the maximum likelihood estimator of the slope and intercept jointly is consistent and asymptotically normal regardless of the null. At the null, the joint maximum likelihood estimator falls along a straight line through the origin with perfect correlation asymptotically to the first order. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 229 236 http://hdl.handle.net/10.1093/biomet/asn059 application/pdf Access to full text is restricted to subscribers. Z. Tan

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:747-7632009-04-18RePEc:oup:biomet

article Our paper proposes adaptive Monte Carlo sampling schemes for Bayesian variable selection in linear regression that improve on standard Markov chain methods. We do so by considering Metropolis--Hastings proposals that make use of accumulated information about the posterior distribution obtained during sampling. Adaptation needs to be done carefully to ensure that sampling is from the correct ergodic distribution. We give conditions for the validity of an adaptive sampling scheme in this problem, and for simulating from a distribution on a finite state space in general, and suggest a class of adaptive proposal densities which uses best linear prediction to approximate the Gibbs sampler. Our sampling scheme is computationally much faster per iteration than the Gibbs sampler, and when this is taken into account the efficiency gains when using our sampling scheme compared to alternative approaches are substantial in terms of precision of estimation of posterior quantities of interest for a given amount of computation time. We compare our method with other sampling schemes for examples involving both real and simulated data. The methodology developed in the paper can be extended to variable selection in more general problems. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 747 763 http://hdl.handle.net/10.1093/biomet/92.4.747 text/html Access to full text is restricted to subscribers. David J. Nott Robert Kohn

oai:RePEc:oup:biomet:v:92:y:2005:i:3:p:679-6902009-04-18RePEc:oup:biomet

article We present an orthonormal bases approach for detecting general differences among continuous distributions. An unknown density function is represented by a finite vector of its estimated Fourier coefficients with respect to a suitable orthonormal basis. For a wide class of orthonormal bases, we establish asymptotic normality of the vector of estimated Fourier coefficients and propose an unbiased and consistent estimator of its asymptotic covariance matrix. Fourier coeffients are modelled as functions of fixed and possibly random effects. This approach allows simultaneous detection of distributional differences attributable to various factors in clustered and correlated data with suffciently large numbers of observations per each cluster with the same fixed and random effects realisations. This work was motivated by multi-level clustered non-Gaussian datasets from genetic studies. Copyright 2005, Oxford University Press. 3 2005 92 September Biometrika 679 690 http://hdl.handle.net/10.1093/biomet/92.3.679 text/html Access to full text is restricted to subscribers. Inna Chervoneva Boris Iglewicz

oai:RePEc:oup:biomet:v:95:y:2008:i:4:p:1002-10052009-04-18RePEc:oup:biomet

article Some preliminary comments are made about the reasons for combining component observations into composite or derived variables. A method for forming derived variables sensitive to specified changes in the underlying multivariate distribution is described and illustrated by an issue in a study of animal pathology. Copyright 2008, Oxford University Press. 4 2008 95 Biometrika 1002 1005 http://hdl.handle.net/10.1093/biomet/asn040 application/pdf Access to full text is restricted to subscribers. D. R. Cox

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:745-7542009-04-18RePEc:oup:biomet

article Rejection sampling thins out samples from a candidate density from which it is easy to simulate, to obtain samples from a more awkward target density. A prerequisite is knowledge of the finite supremum of the ratio of the target and candidate densities. This severely restricts application of the method because it can be difficult to calculate the supremum. We use theoretical argument and numerical work to show that a practically perfect sample may be obtained by replacing the exact supremum with the maximum obtained from simulated candidates. We also provide diagnostics for failure of the method caused by a bad choice of candidate distribution. The implication is that essentially no theoretical work is required to apply rejection sampling in many practical cases. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 745 754 Brian S. Caffo

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:687-7042009-04-18RePEc:oup:biomet

article We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the model explains well the common characteristics of log-returns. We propose a new wavelet thresholding algorithm for volatility estimation in this model, in which Haar wavelets are combined with the variance-stabilising Fisz transform. The resulting volatility estimator is mean-square consistent with a near-parametric rate, does not require any pre-estimates, is rapidly computable and is easily implemented. We also discuss important variations on the choice of estimation parameters. We show that our approach both gives a very good fit to selected currency exchange datasets, and achieves accurate long- and short-term volatility forecasts in comparison to the GARCH(1, 1) and moving window techniques. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 687 704 http://hdl.handle.net/10.1093/biomet/93.3.687 text/html Access to full text is restricted to subscribers. Piotr Fryzlewicz Theofanis Sapatinas Suhasini Subba Rao

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:451-4642009-04-18RePEc:oup:biomet

article In this paper we derive general formulae suitable for Monte Carlo computation of conditional expectations of functions of a random vector given a sufficient statistic. The problem of direct sampling from the conditional distribution is considered in particular. It is shown that this can be done by a simple parameter adjustment of the original statistical model, provided the model has a certain pivotal structure. A connection with a classical problem regarding fiducial and posterior distributions is pointed out. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 451 464 http://hdl.handle.net/10.1093/biomet/92.2.451 text/html Access to full text is restricted to subscribers. Bo Henry Lindqvist Gunnar Taraldsen

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:809-8252009-04-18RePEc:oup:biomet

article We present an approach to Bayesian model selection for finitely observed diffusion processes. We use data augmentation by treating the paths between observed points as missing data. For a fixed model formulation, the strong dependence between the missing paths and the volatility of the diffusion can be broken down by adopting the method of Roberts & Stramer (2001). We describe how this method may be extended to the case of model selection via reversible jump Markov chain Monte Carlo. In addition we extend the formulation of a diffusion model to capture a potential non-Markov state dependence in the drift. Issues of appropriate choices of priors and efficient transdimensional proposal distributions for the reversible jump algorithm are also addressed. The approach is illustrated using simulated data and an example from finance. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 809 825 http://hdl.handle.net/10.1093/biomet/93.4.809 text/html Access to full text is restricted to subscribers. Petros Dellaportas Nial Friel Gareth O. Roberts

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:679-6942009-04-18RePEc:oup:biomet

article Under the assumption of proportional hazards, the log-rank test is optimal for testing the null hypothesis <inline-formula><inline-graphic xlink:href="asn003ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula>, where <inline-formula><inline-graphic xlink:href="asn003ilm2.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> denotes the logarithm of the hazard ratio. However, if there are additional covariates that correlate with survival times, making use of their information will increase the efficiency of the log-rank test. We apply the theory of semiparametrics to characterize a class of regular and asymptotically linear estimators for <inline-formula><inline-graphic xlink:href="asn003ilm3.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> when auxiliary covariates are incorporated into the model, and derive estimators that are more efficient. The Wald tests induced by these estimators are shown to be more powerful than the log-rank test. Simulation studies are used to illustrate the gains in efficiency. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 679 694 http://hdl.handle.net/10.1093/biomet/asn003 application/pdf Access to full text is restricted to subscribers. Xiaomin Lu Anastasios A. Tsiatis

oai:RePEc:oup:biomet:v:91:y:2004:i:3:p:543-5582009-04-18RePEc:oup:biomet

article In this paper we propose inference methods based on the EM algorithm for estimating the parameters of a weakly parameterised competing risks model with masked causes of failure and second-stage data. With a carefully chosen definition of complete data, the maximum likelihood estimation of the cause-specific hazard functions and of the masking probabilities is performed via an EM algorithm. Both the E- and M-steps can be solved in closed form under the full model and under some restricted models of interest. We illustrate the flexibility of the method by showing how grouped data and tests of common hypotheses in the literature on missing cause of death can be handled. The method is applied to a real dataset and the asymptotic and robustness properties of the estimators are investigated through simulation. Copyright Biometrika Trust 2004, Oxford University Press. 3 2004 91 September Biometrika 543 558 Radu V. Craiu

oai:RePEc:oup:biomet:v:94:y:2007:i:1:p:153-1652009-04-18RePEc:oup:biomet

article We propose an estimating function for parameters in a model for Poisson process intensity when time- or space-varying covariates are observed for both the events of the process and at sample times or locations selected from a probability-based sampling design. We investigate the large-sample properties of the proposed estimator under increasing domain asymptotics, demonstrating that it is consistent and asymptotically normally distributed. We illustrate our approach using data from an ecological momentary assessment of smoking. Copyright 2007, Oxford University Press. 1 2007 94 Biometrika 153 165 http://hdl.handle.net/10.1093/biomet/asm009 application/pdf Access to full text is restricted to subscribers. Stephen L. Rathbun Saul Shiffman Chad J. Gwaltney

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:451-4672009-04-18RePEc:oup:biomet

article We study tools for checking the validity of a parametric regression model. When the dimension of the regressors is large, many of the existing tests face the curse of dimensionality or require some ordering of the data. Our tests are based on the residual empirical process marked by proper functions of the regressors. They are able to detect local alternatives converging to the null at parametric rates. Parametric and nonparametric alternatives are considered. In the latter case, through a proper principal component decomposition, we are able to derive smooth directional tests which are asymptotically distribution-free under the null model. The new tests take into account precisely the 'geometry of the model'. A simulation study is carried through and an application to a real dataset is illustrated. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 451 467 http://hdl.handle.net/10.1093/biomet/asm095 application/pdf Access to full text is restricted to subscribers. W. Stute W. L. Xu L. X. Zhu

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:724-7272009-04-18RePEc:oup:biomet

article It is well known that, without the assumption of independence between two nonnegative random variables X and Y, the survival function of X is not identifiable on the basis of the joint distribution function of Z &equals; min(X, Y) and &dgr; &equals; I(Z &equals; Y). In this paper, we provide a simple condition in the form of conditional distribution of Y given X. We show that our condition is equivalent to the constant-sum condition proposed by Williams & Lagakos (1977). As a result the survival function of X can be identified from the joint distribution of Z and &dgr; and the Kaplan--Meier estimator with Greenwood's formula for its variance remains valid. Examples which satisfy the condition are given. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 724 727 Nader Ebrahimi

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:745-7542009-04-18RePEc:oup:biomet

article Following Cox & Wermuth (1994, 2002), we show that the distribution of a set of binary observable variables, induced by a certain discrete latent variable model, may be approximated by a quadratic exponential distribution. This discrete latent variable model is equivalent to the latent-class version of the two-parameter logistic model of Birnbaum (1968), which may be seen as a generalized version of the Rasch model (Rasch, 1960, 196). On the basis of this result, we develop an approximate maximum likelihood estimator of the item parameters of the two-parameter logistic model which is very simply implemented. The proposed approach is illustrated through an example based on a dataset on educational assessment. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 745 754 http://hdl.handle.net/10.1093/biomet/asm045 application/pdf Access to full text is restricted to subscribers. Francesco Bartolucci Fulvia Pennoni

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:99-1122009-04-18RePEc:oup:biomet

article Traditionally the neighbourhood size k in the k-nearest-neighbour algorithm is either fixed at the first nearest neighbour or is selected on the basis of a crossvalidation study. In this paper we present an alternative approach that develops the k-nearest-neighbour algorithm using likelihood-based inference. Our method takes the form of a generalised linear regression on a set of k-nearest-neighbour autocovariates. By defining the k-nearest-neighbour algorithm in this way we are able to extend the method to accommodate the original predictor variables as possible linear effects as well as allowing for the inclusion of multiple nearest-neighbour terms. The choice of the final model proceeds via a stepwise regression procedure. It is shown that our method incorporates a conventional generalised linear model and a conventional k-nearest-neighbour algorithm as special cases. Empirical results suggest that the method out-performs the standard k-nearest-neighbour method in terms of misclassification rate on a wide variety of datasets. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 99 112 Christopher C. Holmes

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:63-742009-04-18RePEc:oup:biomet

article A common objective in longitudinal studies is the investigation of the association structure between a longitudinal response process and the time to an event of interest. An attractive paradigm for the joint modelling of longitudinal and survival processes is the shared parameter framework, where a set of random effects is assumed to induce their interdependence. In this work, we propose an alternative parameterization for shared parameter models and investigate the effect of misspecifying the random effects distribution in the parameter estimates and their standard errors. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 63 74 http://hdl.handle.net/10.1093/biomet/asm087 application/pdf Access to full text is restricted to subscribers. Dimitris Rizopoulos Geert Verbeke Geert Molenberghs

oai:RePEc:oup:biomet:v:95:y:2008:i:1:p:241-2472009-04-18RePEc:oup:biomet

article We propose an efficient and adaptive shrinkage method for variable selection in the Cox model. The method constructs a piecewise-linear regularization path connecting the maximum partial likelihood estimator and the origin. Then a model is selected along the path. We show that the constructed path is adaptive in the sense that, with a proper choice of regularization parameter, the fitted model works as well as if the true underlying submodel were given in advance. A modified algorithm of the least-angle-regression type efficiently computes the entire regularization path of the new estimator. Furthermore, we show that, with a proper choice of shrinkage parameter, the method is consistent in variable selection and efficient in estimation. Simulation shows that the new method tends to outperform the lasso and the smoothly-clipped-absolute-deviation estimators with moderate samples. We apply the methodology to data concerning nursing homes. Copyright 2008, Oxford University Press. 1 2008 95 Biometrika 241 247 http://hdl.handle.net/10.1093/biomet/asm083 application/pdf Access to full text is restricted to subscribers. Hui Zou

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:521-5372009-04-22RePEc:oup:biomet

article In some cases model-based and model-assisted inferences can lead to very different estimators. These two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator, a strategy being a pair composed of a sampling design and an estimator. We show that, under a linear model, the optimal model-assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the Horvitz--Thompson estimator. If the heteroscedasticity of the model is &lsquor;fully explainable&rsquor; by the auxiliary variables, then this strategy is also optimal in a model-based sense. Moreover, under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model, the best linear unbiased estimator and the Horvitz--Thompson estimator are equal. Finally, it is possible to construct a single estimator for both the design and model variance. The inference can thus be valid under the sampling design and under the model. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 521 537 http://hdl.handle.net/10.1093/biomet/asn027 application/pdf Access to full text is restricted to subscribers. Desislava Nedyalkova Yves Tillé

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:877-8932009-04-22RePEc:oup:biomet

article The increased collection of high-dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures. In this paper, we propose a model-based method that addresses the two problems simultaneously. We introduce a latent binary vector to identify discriminating variables and use Dirichlet process mixture models to define the cluster structure. We update the variable selection index using a Metropolis algorithm and obtain inference on the cluster structure via a split-merge Markov chain Monte Carlo technique. We explore the performance of the methodology on simulated data and illustrate an application with a DNA microarray study. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 877 893 http://hdl.handle.net/10.1093/biomet/93.4.877 text/html Access to full text is restricted to subscribers. Sinae Kim Mahlet G. Tadesse Marina Vannucci

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:1011-10172009-04-22RePEc:oup:biomet

article The multivariate logistic transform is a reparameterisation of cell probabilities in terms of marginal logistic contrasts. It is known that an arbitrary set of logistic contrasts may not correspond to a valid joint distribution. In this paper we present an efficient algorithm for detecting whether or not the inverse transform exists, and for computing it if it does. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 1011 1017 http://hdl.handle.net/10.1093/biomet/93.4.1011 text/html Access to full text is restricted to subscribers. Bahjat F. Qaqish Anastasia Ivanova

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:211-2242009-04-22RePEc:oup:biomet

article <?Pub Caret> This paper treats some examples where likelihood-based inference for certain model parameters may produce empty confidence sets. The first example concerns epidemics, and the parameter of interest is the basic reproduction number R-sub-0, which is to be estimated from the final size of an epidemic in a finite population. The second example treats estimation of the mean of the offspring distribution in a branching process, based on observing the total progeny, i.e. the total number of individuals ever born in the branching process. The final example considers estimation of the linear drift in a Brownian motion, based on observing the first hitting time of some horizontal barrier. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 211 224 Frank G Ball

oai:RePEc:oup:biomet:v:89:y:2002:i:2:p:478-4832009-04-22RePEc:oup:biomet

article Edwards & Lauritzen (2001) have recently proposed the TM algorithm for finding the maximum likelihood estimate when the likelihood can be truly or artificially regarded as a conditional likelihood, and the full likelihood is more easily maximised. They have presented a proof of convergence, provided that the algorithm is supplemented by a line search. In this note a simple expression, in terms of observed information matrices, is given for the convergence rate of the algorithm per se, when it converges, and the result elucidates also in which situations the algorithm will require a line search. Essentially these are cases when the full model does not adequately fit the data. Copyright Biometrika Trust 2002, Oxford University Press. 2 2002 89 June Biometrika 478 483 Rolf Sundberg

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:341-3532009-04-22RePEc:oup:biomet

article A broad class of <?Pub Caret>rank-based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations. The corresponding estimators can be obtained via linear programming, and are shown to be consistent and asymptotically normal. The limiting covariance matrices can be estimated by a resampling technique, which does not involve nonparametric density estimation or numerical derivatives. The new estimators represent consistent roots of the non-monotone estimating equations based on the familiar weighted log-rank statistics. Simulation studies demonstrate that the proposed methods perform well in practical settings. Two real examples are provided. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 341 353 Zhezhen Jin

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:777-7902009-04-22RePEc:oup:biomet

article We study the nonparametric k-sample test problem with panel count data. The asymptotic normality of a smooth functional of the nonparametric maximum pseudo-likelihood estimator (Wellner & Zhang, 2000) is established under some mild conditions. We construct a class of easy-to-implement nonparametric tests for comparing mean functions of k populations based on this asymptotic normality. We conduct various simulations to validate and compare the tests. The simulations show that the tests perform quite well and generally have good power to detect differences among the mean functions. The method is illustrated with a real-life example. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 777 790 http://hdl.handle.net/10.1093/biomet/93.4.777 text/html Access to full text is restricted to subscribers. Ying Zhang

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:481-4852009-04-22RePEc:oup:biomet

article Semiparametric methods were proposed by Wei et al. (1989) to analyse recurring event-time data. They modelled the marginal distribution of each event time with a Cox proportional hazards model without imposing any constraint on the joint distribution of different event times. Therefore, it is unclear whether or not event times can simultaneously satisfy their respective marginal proportional hazards assumptions, while having continuous joint distribution. Often this leads to a difficulty of conducting simulation studies. In this note we construct parametric marginal proportional hazards models for recurring event times with proper joint density functions. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 481 485 http://hdl.handle.net/10.1093/biomet/93.2.481 text/html Access to full text is restricted to subscribers. Nader Ebrahimi

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:201-2112009-04-22RePEc:oup:biomet

article Fuzzy multiple comparisons procedures are introduced as a solution to the problem of multiple comparisons for discrete test statistics. The critical function of the randomized p-values is proposed as a measure of evidence against the null hypotheses. The classical concept of randomized tests is extended to multiple comparisons. This approach makes all theory of multiple comparisons developed for continuously distributed statistics automatically applicable to the discrete case. Examples of familywise error rate and false discovery rate procedures are discussed and an application to linkage disequilibrium testing is given. Software for implementing the procedures is available. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 201 211 http://hdl.handle.net/10.1093/biomet/asn061 application/pdf Access to full text is restricted to subscribers. Elena Kulinskaya Alex Lewin

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:295-3052009-04-22RePEc:oup:biomet

article Under the model of independent test statistics, we propose a two-parameter family of Bayes multiple testing procedures. The two parameters can be viewed as tuning parameters. Using the Benjamini--Hochberg step-up procedure for controlling false discovery rate as a baseline for conservativeness, we choose the tuning parameters to compromise between the operating characteristics of that procedure and a less conservative procedure that focuses on alternatives that a priori might be considered likely or meaningful. The Bayes procedures do not have the theoretical and practical shortcomings of the popular stepwise procedures. In terms of the number of mistakes, simulations for two examples indicate that over a large segment of the parameter space, the Bayes procedure is preferable to the step-up procedure. Another desirable feature of the procedures is that they are computationally feasible for any number of hypotheses. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 295 305 http://hdl.handle.net/10.1093/biomet/asn013 application/pdf Access to full text is restricted to subscribers. Arthur Cohen H. B. Sackrowitz Minya Xu Steven Buyske

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:248-2482009-04-22RePEc:oup:biomet

article 1 2009 96 Biometrika 248 248 http://hdl.handle.net/10.1093/biomet/asn065 application/pdf Access to full text is restricted to subscribers. H. He

oai:RePEc:oup:biomet:v:89:y:2002:i:4:p:952-9572009-04-22RePEc:oup:biomet

article The paper considers priors which are right invariant with respect to the Haar measure. It is shown that the posterior coverage probabilities of certain invariant Bayesian predictive regions exactly match the corresponding frequentist probabilities. Several examples are given to illustrate the main result. Copyright Biometrika Trust 2002, Oxford University Press. 4 2002 89 December Biometrika 952 957 Thomas A. Severini

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:213-2202009-04-22RePEc:oup:biomet

article We introduce two new variance estimation procedures that use non-overlapping and overlapping blocks, respectively. The non-overlapping blocks estimator can be viewed as the limit of the thinned block bootstrap estimator recently proposed in Guan Loh (2007), by letting the number of thinned processes and bootstrap samples therein both increase to infinity. The non-overlapping blocks estimator can be obtained quickly since it does not require any thinning or bootstrap steps, and it is more stable. The overlapping blocks estimator further improves the performance of the non-overlapping blocks with a modest increase in computation time. A simulation study demonstrates the superiority of the proposed estimators over the thinned block bootstrap estimator. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 213 220 http://hdl.handle.net/10.1093/biomet/asn072 application/pdf Access to full text is restricted to subscribers. Yongtao Guan

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:303-3172009-04-22RePEc:oup:biomet

article We discuss two methods of making nonparametric Bayesian inference on probability measures subject to a partial stochastic ordering. The first method involves a nonparametric prior for a measure on partially ordered latent observations, and the second involves rejection sampling. Computational approaches are discussed for each method, and interpretations of prior and posterior information are discussed. An application is presented in which inference is made on the number of independently segregating quantitative trait loci present in an animal population. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 303 317 Peter D. Hoff

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:513-5282009-04-22RePEc:oup:biomet

article A method is developed for fitting smooth curves through a series of shapes of landmarks in two dimensions using unrolling and unwrapping procedures in Riemannian manifolds. An explicit method of calculation is given which is analogous to that of Jupp & Kent (1987) for spherical data. The resulting splines are called shape-space smoothing splines. The method resembles that of fitting smoothing splines in real spaces in that, if the smoothing parameter is zero, the resulting curve interpolates the data points, and if it is infinitely large the curve is a geodesic line. The fitted path to the data is defined such that its unrolled version at the tangent space of the starting point is a cubic spline fitted to the unwrapped data with respect to that path. Computation of the fitted path consists of an iterative procedure which converges quickly, and the resulting path is given in a discretised form in terms of a piecewise geodesic path. The procedure is applied to the analysis of some human movement data, and a test for the appropriateness of a mean geodesic curve is given. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 513 528 http://hdl.handle.net/10.1093/biomet/asm047 application/pdf Access to full text is restricted to subscribers. Alfred Kume Ian L. Dryden Huiling Le

oai:RePEc:oup:biomet:v:94:y:2007:i:2:p:415-4262009-04-22RePEc:oup:biomet

article We present a new class of statistical models, designed for life history analysis of plants and animals, that allow joint analysis of data on survival and reproduction over multiple years, allow for variables having different probability distributions, and correctly account for the dependence of variables on earlier variables. We illustrate their utility with an analysis of data taken from an experimental study of Echinacea angustifolia sampled from remnant prairie populations in western Minnesota. These models generalize both generalized linear models and survival analysis. The joint distribution is factorized as a product of conditional distributions, each an exponential family with the conditioning variable being the sample size of the conditional distribution. The model may be heterogeneous, each conditional distribution being from a different exponential family. We show that the joint distribution is from a flat exponential family and derive its canonical parameters, Fisher information and other properties. These models are implemented in an R package 'aster' available from the Comprehensive R Archive Network, CRAN. Copyright 2007, Oxford University Press. 2 2007 94 Biometrika 415 426 http://hdl.handle.net/10.1093/biomet/asm030 application/pdf Access to full text is restricted to subscribers. Charles J. Geyer Stuart Wagenius Ruth G. Shaw

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:77-932009-04-22RePEc:oup:biomet

article Despite the well-known difficulties of undertaking inference with mixture models, they are frequently used for modelling. These inferential problems arise because the underlying geometry of a mixture family is very complicated. This paper shows that by adding a simplifying assumption, which frequently is natural statistically, the geometric structure is reduced to a much more tractable form. This enables standard inferential techniques to be applied successfully. One result of studying the local geometry is that it unifies the convex and differential geometric theories of mixture models. The techniques proposed are applied to prediction, random effects and measurement error models. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 77 93 Paul Marriott

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:95-1102009-04-22RePEc:oup:biomet

article Given aggregated longitudinal data generated by a Markov chain, which may be nonhomogeneous, the problem considered is that of modelling, estimating and interpolating the logarithms of partial odds and hence the transition probabilities. By partial odds is meant the probability of a transition to another state divided by the probability of no transition. A result establishing asymptotic normality leads to vector weighted least squares estimation of parameterised partial odds using standard regression methods. It is shown how to obtain estimates of one-step transition probabilities from widely or irregularly spaced data. The methods are illustrated on an example concerning competing causes of death. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 95 110 B. A. Davis

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:305-3192009-04-22RePEc:oup:biomet

article In a case-cohort design introduced by Prentice (1986), covariates are assembled only for a subcohort randomly selected from the entire cohort, and any additional cases outside the subcohort. Semiparametric transformation models are considered here for failure time data from the case-cohort design. Weighted estimating equations are proposed for estimation of the regression parameters. The estimation procedure of survival probability at given covariate levels is also provided. Asymptotic properties are derived for the estimators using finite population sampling theory, U-statistics theory and martingale convergence results. The finite-sample properties of the proposed estimators, as well as the efficiency relative to the full cohort estimators, are assessed via simulation studies. A case-cohort dataset from the Atherosclerosis Risk in Communities study is used to illustrate the estimating procedure. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 305 319 Lan Kong

oai:RePEc:oup:biomet:v:90:y:2003:i:1:p:171-1822009-04-22RePEc:oup:biomet

article Sequentially-administered diagnostic tests used to determine the occurrence of a silent event are sometimes subject to error, leading to false positive and false negative test results. In such cases, standard methods for interval censored data do not give valid estimates of the distribution of the time to the event. We present methods for estimating the distribution of the time to the event that account for multiple types of imperfect diagnostic test, as well as differing periods at risk. We illustrate the methods with simulated data and results from a clinical trial for the prevention of mother-to-infant transmission of HIV in Tanzania. Copyright Biometrika Trust 2003, Oxford University Press. 1 2003 90 March Biometrika 171 182 R. Balasubramanian

oai:RePEc:oup:biomet:v:92:y:2005:i:2:p:465-4762009-04-22RePEc:oup:biomet

article The Fisher--Bingham distribution is obtained when a multivariate normal random vector is conditioned to have unit length. Its normalising constant can be expressed as an elementary function multiplied by the density, evaluated at 1, of a linear combination of independent noncentral χ-sub-1-super-2 random variables. Hence we may approximate the normalising constant by applying a saddlepoint approximation to this density. Three such approximations, implementation of each of which is straightforward, are investigated: the first-order saddlepoint density approximation, the second-order saddlepoint density approximation and a variant of the second-order approximation which has proved slightly more accurate than the other two. The numerical and theoretical results we present showthat this approach provides highly accurate approximations in a broad spectrum of cases. Copyright 2005, Oxford University Press. 2 2005 92 June Biometrika 465 476 http://hdl.handle.net/10.1093/biomet/92.2.465 text/html Access to full text is restricted to subscribers. A. Kume Andrew T. A. Wood

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:211-2182009-04-22RePEc:oup:biomet

article For a stationary time series, Whittle constructed a likelihood for the spectral density based on the approximate independence of the discrete Fourier transforms of the data at certain frequencies. Whittle's likelihood has been widely used in the literature for constructing estimators. In this paper, we show that, for a Gaussian time series, the Whittle measure is mutually contiguous with the actual distribution of the data. As a consequence, most asymptotic properties of estimators and test statistics derived under the Whittle measure can be carried over to the actual distribution. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 211 218 Nidhan Choudhuri

oai:RePEc:oup:biomet:v:93:y:2006:i:3:p:537-5542009-04-22RePEc:oup:biomet

article A Gaussian copula regression model gives a tractable way of handling a multivariate regression when some of the marginal distributions are non-Gaussian. Our paper presents a general Bayesian approach for estimating a Gaussian copula model that can handle any combination of discrete and continuous marginals, and generalises Gaussian graphical models to the Gaussian copula framework. Posterior inference is carried out using a novel and efficient simulation method. The methods in the paper are applied to simulated and real data. Copyright 2006, Oxford University Press. 3 2006 93 September Biometrika 537 554 http://hdl.handle.net/10.1093/biomet/93.3.537 text/html Access to full text is restricted to subscribers. Michael Pitt David Chan Robert Kohn

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:125-1402009-04-22RePEc:oup:biomet

article The likelihood-based influence analysis methodology introduced in Cook (1986) uses a parameterised space of local perturbations of a base model. It is frequently the case that such perturbation schemes involve more parameters of interest and perturbation parameters than there are observations, and hence the perturbation space is often explored rather than estimated, where exploration means discovering the effect on inference of putatively choosing values of perturbation parameters. This paper considers the question of what can be learned about the perturbation parameters through the data. It extends Cook's methodology to take account of information available in the data regarding the perturbations, the general philosophy of the approach being that of learn what you can and explore what you cannot learn. Both local and global analyses are possible, as indicated by the data, while the eigenvector sign indeterminacy of local analysis is removed. Numerical examples are given and further developments are briefly indicated. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 125 140 Frank Critchley

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:135-1482009-04-22RePEc:oup:biomet

article If Fourier series are used as the basis for inference in deconvolution problems, the effects of the errors factorise out in a way that is easily exploited empirically. This property is the consequence of elementary addition formulae for sine and cosine functions, and is not readily available when one is using methods based on other orthogonal series or on continuous Fourier transforms. It allows relatively simple estimators to be constructed, founded on the addition of finite series rather than on integration. The performance of these methods can be particularly effective when edge effects are involved, since cosine series estimators are quite resistant to boundary problems. In this context we point to the advantages of trigonometric-series methods for density deconvolution; they have better mean squared error performance when edge effects are involved, they are particularly easy to code, and they admit a simple approach to empirical choice of smoothing parameter, in which a version of thresholding, familiar in wavelet-based inference, is used in place of conventional smoothing. Applications to other deconvolution problems are briefly discussed. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 135 148 http://hdl.handle.net/10.1093/biomet/92.1.135 text/html Access to full text is restricted to subscribers. Peter Hall Peihua Qiu

oai:RePEc:oup:biomet:v:93:y:2006:i:2:p:357-3662009-04-22RePEc:oup:biomet

article We suggest a completely empirical approach to the construction of confidence bands for hazard functions, based on smoothing the Nelsen-Aalen estimator. In particular, we introduce a local bandwidth-choice method. Our approach uses empirical information about both the survival rate and the censoring rate, and employs undersmoothing to alleviate difficulties caused by bias. We use both Edgeworth expansion and numerical simulation, the former to develop a basic formula and the latter to modify it for general use. Copyright 2006, Oxford University Press. 2 2006 93 June Biometrika 357 366 http://hdl.handle.net/10.1093/biomet/93.2.357 text/html Access to full text is restricted to subscribers. Ming-Yen Cheng Peter Hall Dongsheng Tu

oai:RePEc:oup:biomet:v:93:y:2006:i:1:p:41-522009-04-22RePEc:oup:biomet

article We propose a class of estimators of the Bayes factor which is based on an extension of the bridge sampling identity of Meng & Wong (1996) and makes use of the output of the reversible jump algorithm of Green (1995). Within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models. The proposed estimators are very easily computed and lead to a substantial gain of efficiency in estimating the Bayes factor over the standard estimator based on the reversible jump output. This is illustrated through a series of Monte Carlo simulations involving a linear and a logistic regression model. Copyright 2006, Oxford University Press. 1 2006 93 March Biometrika 41 52 http://hdl.handle.net/10.1093/biomet/93.1.41 text/html Access to full text is restricted to subscribers. Francesco Bartolucci Luisa Scaccia Antonietta Mira

oai:RePEc:oup:biomet:v:91:y:2004:i:1:p:113-1232009-04-22RePEc:oup:biomet

article We propose a test for multimodality with dependent data by resampling from a suitably constructed transition probability kernel, which includes Silverman's test with independent data as a special case. We extend some theoretical properties of Silverman's test with independent and identically distributed data to weakly dependent data, and also discuss the robustness of Silverman's test against departure from independence. Copyright Biometrika Trust 2004, Oxford University Press. 1 2004 91 March Biometrika 113 123 K. S. Chan

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:335-3492009-04-22RePEc:oup:biomet

article Motivated by the modelling of non-Gaussian data or positively correlated data on a lattice, extensions of Besag's automodels to exponential families with multi-dimensional parameters have been proposed recently. We provide a multiple-parameter analogue of Besag's one-dimensional result that gives the necessary form of the exponential families for the Markov random field's conditional distributions. We propose estimation of parameters by maximum pseudolikelihood and give a proof of the consistency of the estimators for the multi-parameter automodel. The methodology is illustrated with examples, in particular the building of a cooperative system with beta conditional distributions. We also indicate future applications of these models to the analysis of mixed-state spatial data. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 335 349 http://hdl.handle.net/10.1093/biomet/asn016 application/pdf Access to full text is restricted to subscribers. Cécile Hardouin Jian-Feng Yao

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:455-4632009-04-22RePEc:oup:biomet

article We introduce a family of multivariate binary distributions with certain conditional linear property. This family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 455 463 Bahjat F. Qaqish

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:773-7782009-04-22RePEc:oup:biomet

article The conventional model selection criterion, the Akaike information criterion, <sc>aic</sc>, has been applied to choose candidate models in mixed-effects models by the consideration of marginal likelihood. Vaida & Blanchard (2005) demonstrated that such a marginal <sc>aic</sc> and its small sample correction are inappropriate when the research focus is on clusters. Correspondingly, these authors suggested the use of conditional <sc>aic</sc>. Their conditional <sc>aic</sc> is derived under the assumption that the variance-covariance matrix or scaled variance-covariance matrix of random effects is known. This note provides a general conditional <sc>aic</sc> but without these strong assumptions. Simulation studies show that the proposed method is promising. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 773 778 http://hdl.handle.net/10.1093/biomet/asn023 application/pdf Access to full text is restricted to subscribers. Hua Liang Hulin Wu Guohua Zou

oai:RePEc:oup:biomet:v:90:y:2003:i:3:p:728-7312009-04-22RePEc:oup:biomet

article The contributions of Ernest Lhoste are largely unknown outside France, and even within that country are not well known. His important contributions were in the two areas of the development of prior distributions that represent little or no information, and a sophisticated posterior analysis for normal and binomial populations. His results are similar to those of Haldane (1948) and Jeffreys (1961), but they appeared much earlier, in 1923. He gave a great deal of thought to how to represent vague prior knowledge and his results represent a significant and unique contribution to Bayesian ideas in the early part of the 20th century. Copyright Biometrika Trust 2003, Oxford University Press. 3 2003 90 September Biometrika 728 731 Lyle Broemeling

oai:RePEc:oup:biomet:v:89:y:2002:i:1:p:23-372009-04-22RePEc:oup:biomet

article Case-control samples allow straightforward calculation of estimates of the association between covariates and disease status by fitting a prospective logistic regression model. In genetic studies of disease, investigators often gather additional information on response and covariate variables from family members of cases and controls. The objective is to model the responses of all the family members in terms of the covariate data. Whittemore (1995) has discussed maximum likelihood methods for fitting a special class of logistic models to family data collected according to a particular design. In the present paper, we show that we can obtain efficient semiparametric maximum likelihood estimates for an arbitrary multivariate binary regression model by fitting a modified prospective model for a wide class of retrospective designs. However, in contrast to the situation with simple case-control studies, the prospective model will differ from the original model even when the model is logistic. Copyright Biometrika Trust 2002, Oxford University Press. 1 2002 89 March Biometrika 23 37 J. Neuhaus

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:709-7182009-04-22RePEc:oup:biomet

article We consider experimental designs in a regression set-up where the unknown regression function belongs to a known family of nested linear models. The objective of our design is to select the correct model from the family of nested models as well as to estimate efficiently the parameters associated with that model. We show that our proposed design is able to choose the true model with probability tending to one as the number of trials grows to infinity. We also establish that our selected design converges to the optimal design distribution for the true linear model ensuring asymptotic efficiency of least squares estimators of model parameters. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 709 718 Atanu Biswas

oai:RePEc:oup:biomet:v:89:y:2002:i:3:p:699-7082009-04-22RePEc:oup:biomet

article Often in sequential trials some additional data become available after a stopping boundary has been reached. A method for incorporating such information from overrunning is developed, based on a maximum-likelihood ordering of the sample space after overrunning. This yields a p-value for the primary test and a median-unbiased estimator and confidence intervals for the parameter under test. The context is that of observing a Brownian motion with drift, with either linear stopping boundaries in continuous time or discrete-time group-sequential boundaries. The methods apply to many clinical trials and are exemplified with data from a survival-analysis-based sequential clinical trial. Copyright Biometrika Trust 2002, Oxford University Press. 3 2002 89 August Biometrika 699 708 W. J. Hall

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:83-932009-04-22RePEc:oup:biomet

article We propose a general and unified approach to the selection of regular fractional factorial designs, which can be applied to experiments that are unblocked, blocked or have a split-plot structure. Our criterion is derived as a good surrogate for the model-robustness criterion of information capacity. In the case of random block effects, it takes the ratio of intra- and interblock variances into account. In most of the cases we have examined, there exist designs that are optimal for all values of that ratio. Examples of optimal designs that depend on the ratio are provided. We also demonstrate that our criterion can further discriminate designs that cannot be distinguished by the existing minimum-aberration criteria. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 83 93 http://hdl.handle.net/10.1093/biomet/asn066 application/pdf Access to full text is restricted to subscribers. Ching-Shui Cheng Pi-Wen Tsai

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:1018-10242009-04-22RePEc:oup:biomet

article Zhu & Hastie (2003) presented a general criterion for finding discriminant directions. To optimise their criterion, iterative methods are needed unless each class has a Gaussian distribution with a common covariance matrix. In this short paper, we present a slightly more general case where iterative methods can also be avoided. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 1018 1024 http://hdl.handle.net/10.1093/biomet/93.4.1018 text/html Access to full text is restricted to subscribers. Mu Zhu

oai:RePEc:oup:biomet:v:94:y:2007:i:3:p:615-6252009-04-22RePEc:oup:biomet

article In regression with a vector of quantitative predictors, sufficient dimension reduction methods can effectively reduce the predictor dimension, while preserving full regression information and assuming no parametric model. However, all current reduction methods require the sample size n to be greater than the number of predictors p. It is well known that partial least squares can deal with problems with n < p. We first establish a link between partial least squares and sufficient dimension reduction. Motivated by this link, we then propose a new dimension reduction method, entitled partial inverse regression. We show that its sample estimator is consistent, and that its performance is similar to or superior to partial least squares when n < p, especially when the regression model is nonlinear or heteroscedastic. An example involving the spectroscopy analysis of biscuit dough is also given. Copyright 2007, Oxford University Press. 3 2007 94 Biometrika 615 625 http://hdl.handle.net/10.1093/biomet/asm043 application/pdf Access to full text is restricted to subscribers. Lexin Li R. Dennis Cook Chih-Ling Tsai

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:435-4442009-04-22RePEc:oup:biomet

article We provide a general framework for the computationally efficient analysis, both Bayesian and classical, of integrated multi-site recovery&sol;recapture models in the presence of individual-level covariates by extending the basic Arnason--Schwarz models and deriving closed-form likelihood expressions, together with corresponding sufficient statistics. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 435 444 R. King

oai:RePEc:oup:biomet:v:90:y:2003:i:4:p:809-8302009-04-22RePEc:oup:biomet

article A Bayesian method is proposed for estimating an inverse covariance matrix from Gaussian data. The method is based on a prior that allows the off-diagonal elements of the inverse covariance matrix to be zero, and in many applications results in a parsimonious parameterisation of the covariance matrix. No assumption is made about the structure of the corresponding graphical model, so the method applies to both nondecomposable and decomposable graphs. All the parameters are estimated by model averaging using an efficient Metropolis--Hastings sampling scheme. A simulation study demonstrates that the method produces statistically efficient estimators of the covariance matrix, when the inverse covariance matrix is sparse. The methodology is illustrated by applying it to three examples that are high-dimensional relative to the sample size. Copyright Biometrika Trust 2003, Oxford University Press. 4 2003 90 December Biometrika 809 830 Frederick Wong

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:801-8202009-04-22RePEc:oup:biomet

article A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) &equals; Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean μ(t) &equals; E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose a nonparametric maximum likelihood estimator of μ(t). This estimator is shown to be √n-consistent and asymptotically normal under the assumed model and robust to model misspecification. Simulations and a realdata example show that the proposed estimator is competitive with landmark registration, often considered the benchmark, and has the advantage of avoiding time-consuming and often infeasible individual landmark identification. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 801 820 http://hdl.handle.net/10.1093/biomet/92.4.801 text/html Access to full text is restricted to subscribers. Daniel Gervini Theo Gasser

oai:RePEc:oup:biomet:v:92:y:2005:i:4:p:951-9562009-04-22RePEc:oup:biomet

article A simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Consequently, this test can be used when the number of variables is not small relative to the sample size and, in particular, even when the number of variables exceeds the sample size. The finite sample size performance of the normal approximation is evaluated in a simulation study and the results are compared to those of the likelihood ratio test. Copyright 2005, Oxford University Press. 4 2005 92 December Biometrika 951 956 http://hdl.handle.net/10.1093/biomet/92.4.951 text/html Access to full text is restricted to subscribers. James R. Schott

oai:RePEc:oup:biomet:v:92:y:2005:i:1:p:31-462009-04-22RePEc:oup:biomet

article While empirical likelihood has been shown to exhibit many of the properties of conventional parametric likelihoods, a formal probabilistic interpretation has so far been lacking. We show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric Bayesian procedure which places a type of noninformative prior on the space of distributions. This prior gives preference to distributions having a small support and, among those sharing the same support, it favours entropy-maximising distributions. The resulting nonparametric Bayesian procedure admits a computationally convenient representation as an empirical-likelihood-type likelihood where the probability weights are obtained via exponential tilting. The proposed methodology provides an attractive alternative to the Bayesian bootstrap as a nonparametric limit of a Bayesian procedure for moment condition models. Copyright 2005, Oxford University Press. 1 2005 92 March Biometrika 31 46 http://hdl.handle.net/10.1093/biomet/92.1.31 text/html Access to full text is restricted to subscribers. Susanne M. Schennach

oai:RePEc:oup:biomet:v:91:y:2004:i:2:p:251-2622009-04-22RePEc:oup:biomet

article We study the profile-kernel and backfitting methods in partially linear models for clustered&sol;longitudinal data. For independent data, despite the potential root-n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting often produces a larger asymptotic variance than the profile-kernel method&semi; that is, for clustered data, in addition to its bias problem, the backfitting estimator does not have the same asymptotic efficiency as the profile-kernel estimator. Consequently, the common practice of using the backfitting method to compute profile-kernel estimates is no longer advised. We illustrate this in detail by following Zeger & Diggle (1994) and Lin & Carroll (2001) with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for parametric estimation. Numerical performance of the two estimators is investigated through a simulation study. Their application to an ophthalmology dataset is also described. Copyright Biometrika Trust 2004, Oxford University Press. 2 2004 91 June Biometrika 251 262 Zonghui Hu

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:961-9722009-04-22RePEc:oup:biomet

article We propose an isotonic logistic discrimination procedure which generalises linear logistic discrimination by allowing linear boundaries to be more flexibly shaped as monotone functions of the discriminant variables. Under each of three familiar sampling schemes for obtaining a training dataset, namely prospective, mixture and retrospective, we provide the corresponding likelihood-based inference. An application to a cancer study is given. In addition, we consider theoretical comparisons of our method with two recent algorithmic monotone discrimination procedures. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 961 972 http://hdl.handle.net/10.1093/biomet/93.4.961 text/html Access to full text is restricted to subscribers. Sungyoung Auh Allan R. Sampson

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:67-822009-04-22RePEc:oup:biomet

article In industrial experimentation, there is growing interest in studies that span more than one processing step. Convenience often dictates restrictions in randomization in passing from one processing step to another. When the study encompasses three processing steps, this leads to split-split-plot designs. We provide an algorithm for computing D-optimal split-split-plot designs and several illustrative examples. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 67 82 http://hdl.handle.net/10.1093/biomet/asn070 application/pdf Access to full text is restricted to subscribers. Bradley Jones Peter Goos

oai:RePEc:oup:biomet:v:93:y:2006:i:4:p:843-8602009-04-22RePEc:oup:biomet

article We develop a new method for building a hierarchical tree from binary sequence data. It is based on an ancestral mixture model. The sieve parameter in the model plays the role of time in the evolutionary tree of the sequences. By varying the sieve parameter, one can create a hierarchical tree that estimates the population structure at each fixed backward point in time. Application to the clustering of the mitochondrial DNA sequences of Griffiths & Tavare (1994) shows that the approach performs well. Theoretical and computational properties of the ancestral mixture model are further developed. Copyright 2006, Oxford University Press. 4 2006 93 December Biometrika 843 860 http://hdl.handle.net/10.1093/biomet/93.4.843 text/html Access to full text is restricted to subscribers. Shu-Chuan Chen Bruce G. Lindsay

oai:RePEc:oup:biomet:v:95:y:2008:i:3:p:621-6342009-04-22RePEc:oup:biomet

article We consider hypothesis testing with smooth functional data by performing pointwise tests and applying a multiple comparisons procedure. Methods based on general inequalities, such as Bonferroni's method, do not perform well because of the high correlation between observations at nearby points. We consider the multiple comparison procedure proposed by Westfall & Young (1993) and show that it approximates a multiple comparison correction for a continuum of comparisons as the grid for pointwise comparisons becomes finer. Simulations and an application verify that this result applies in practical settings. Copyright 2008, Oxford University Press. 3 2008 95 Biometrika 621 634 http://hdl.handle.net/10.1093/biomet/asn021 application/pdf Access to full text is restricted to subscribers. Dennis D. Cox Jong Soo Lee

oai:RePEc:oup:biomet:v:90:y:2003:i:2:p:319-3262009-04-22RePEc:oup:biomet

article Research has shown that empirical likelihood tests have many of the same asymptotic properties as those derived from parametric likelihoods. This leads naturally to the possibility of using empirical likelihood as the basis for Bayesian inference. Different ways in which this goal might be accomplished are considered. The validity of the resultant posterior inferences is examined, as are frequentist properties of the Bayesian empirical likelihood intervals. Copyright Biometrika Trust 2003, Oxford University Press. 2 2003 90 June Biometrika 319 326 Nicole A. Lazar

oai:RePEc:oup:biomet:v:96:y:2009:i:1:p:107-1172009-04-22RePEc:oup:biomet

article We propose a new method, to construct confidence intervals for spectral mean and related ratio statistics of a stationary process, that avoids direct estimation of their asymptotic variances. By introducing a bandwidth, a self-normalization procedure is adopted and the distribution of the new statistic is asymptotically nuisance-parameter free. The bandwidth is chosen using information criteria and a moving average sieve approximation. Through a simulation study, we demonstrate good finite sample performance of our method when the sample size is moderate, while a comparison with an empirical likelihood-based method for ratio statistics is made, confirming a wider applicability of our method. Copyright 2009, Oxford University Press. 1 2009 96 Biometrika 107 117 http://hdl.handle.net/10.1093/biomet/asn067 application/pdf Access to full text is restricted to subscribers. Xiaofeng Shao

oai:RePEc:oup:biomet:v:91:y:2004:i:4:p:849-8622009-04-22RePEc:oup:biomet

article A semiparametric changepoint model is considered and the empirical likelihood method is applied to detect the change from a distribution to a weighted distribution in a sequence of independent random variables. The maximum likelihood changepoint estimator is shown to be consistent. The empirical likelihood ratio test statistic is proved to have the same limit null distribution as that with parametric models. A data-based test for the validity of the models is also proposed. Simulation shows the sensitivity and robustness of the semiparametric approach. The methods are applied to some classical datasets such as the Nile River data and stock price data. Copyright 2004, Oxford University Press. 4 2004 91 December Biometrika 849 862 http://hdl.handle.net/10.1093/biomet/91.4.849 text/html Access to full text is restricted to subscribers. Zhong Guan

oai:RePEc:oup:biomet:v:95:y:2008:i:2:p:325-3332009-04-22RePEc:oup:biomet

article We develop a Bayesian analysis based on two different Jeffreys priors for the Student-t regression model with unknown degrees of freedom. It is typically difficult to estimate the number of degrees of freedom: improper prior distributions may lead to improper posterior distributions, whereas proper prior distributions may dominate the analysis. We show that Bayesian analysis with either of the two considered Jeffreys priors provides a proper posterior distribution. Finally, we show that Bayesian estimators based on Jeffreys analysis compare favourably to other Bayesian estimators based on priors previously proposed in the literature. Copyright 2008, Oxford University Press. 2 2008 95 Biometrika 325 333 http://hdl.handle.net/10.1093/biomet/asn001 application/pdf