Biometrika - recent issues

Objective Bayesian model selection in Gaussian graphical models

Carvalho, C. M., Scott, J. G. — Thu, 20 Aug 2009 10:00:44 PDT

This paper presents a default model-selection procedure for Gaussian graphical models that involves two new developments. First, we develop a default version of the hyper-inverse Wishart prior for restricted covariance matrices, called the hyper-inverse Wishart g-prior, and show how it corresponds to the implied fractional prior for selecting a graph using fractional Bayes factors. Second, we apply a class of priors that automatically handles the problem of multiple hypothesis testing. We demonstrate our methods on a variety of simulated examples, concluding with a real example analyzing covariation in mutual-fund returns. These studies reveal that the combined use of a multiplicity-correction prior on graphs and fractional Bayes factors for computing marginal likelihoods yields better performance than existing Bayesian methods.

Adaptive regularization using the entire solution surface

Wu, S., Shen, X., Geyer, C. J. — Thu, 20 Aug 2009 10:00:44 PDT

Several sparseness penalties have been suggested for delivery of good predictive performance in automatic variable selection within the framework of regularization. All assume that the true model is sparse. We propose a penalty, a convex combination of the L₁- and L-norms, that adapts to a variety of situations including sparseness and nonsparseness, grouping and nongrouping. The proposed penalty performs grouping and adaptive regularization. In addition, we introduce a novel homotopy algorithm utilizing subgradients for developing regularization solution surfaces involving multiple regularizers. This permits efficient computation and adaptive tuning. Numerical experiments are conducted using simulation. In simulated and real examples, the proposed penalty compares well against popular alternatives.

Asymptotic properties of penalized spline estimators

Claeskens, G., Krivobokova, T., Opsomer, J. D. — Thu, 20 Aug 2009 10:00:44 PDT

We study the class of penalized spline estimators, which enjoy similarities to both regression splines, without penalty and with fewer knots than data points, and smoothing splines, with knots equal to the data points and a penalty controlling the roughness of the fit. Depending on the number of knots, sample size and penalty, we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of smoothing splines, with a clear breakpoint distinguishing the cases. We prove that using fewer knots results in better asymptotic rates than when using a large number of knots. We obtain expressions for bias and variance and asymptotic rates for the number of knots and penalty parameter.

Empirical Bayes estimation for additive hazards regression models

Sinha, D., McHenry, M. B., Lipsitz, S. R., Ghosh, M. — Thu, 20 Aug 2009 10:00:44 PDT

We develop a novel empirical Bayesian framework for the semiparametric additive hazards regression model. The integrated likelihood, obtained by integration over the unknown prior of the nonparametric baseline cumulative hazard, can be maximized using standard statistical software. Unlike the corresponding full Bayes method, our empirical Bayes estimators of regression parameters, survival curves and their corresponding standard errors have easily computed closed-form expressions and require no elicitation of hyperparameters of the prior. The method guarantees a monotone estimator of the survival function and accommodates time-varying regression coefficients and covariates. To facilitate frequentist-type inference based on large-sample approximation, we present the asymptotic properties of the semiparametric empirical Bayes estimates. We illustrate the implementation and advantages of our methodology with a reanalysis of a survival dataset and a simulation study.

Improving point and interval estimators of monotone functions by rearrangement

Chernozhukov, V., Fernandez-Val, I., Galichon, A. — Thu, 20 Aug 2009 10:00:44 PDT

Suppose that a target function is monotonic and an available original estimate of this target function is not monotonic. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function. Furthermore, suppose an original confidence interval, which covers the target function with probability at least 1-, is defined by an upper and lower endpoint functions that are not monotonic. Then the rearranged confidence interval, defined by the rearranged upper and lower endpoint functions, is monotonic, shorter in length in common norms than the original interval, and covers the target function with probability at least 1-. We illustrate the results with a growth chart example.

Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data

Johnson, L. M., Strawderman, R. L. — Thu, 20 Aug 2009 10:00:44 PDT

This paper extends the induced smoothing procedure of Brown & Wang (2006) for the semiparametric accelerated failure time model to the case of clustered failure time data. The resulting procedure permits fast and accurate computation of regression parameter estimates and standard errors using simple and widely available numerical methods, such as the Newton–Raphson algorithm. The regression parameter estimates are shown to be strongly consistent and asymptotically normal; in addition, we prove that the asymptotic distribution of the smoothed estimator coincides with that obtained without the use of smoothing. This establishes a key claim of Brown & Wang (2006) for the case of independent failure time data and also extends such results to the case of clustered data. Simulation results show that these smoothed estimates perform as well as those obtained using the best available methods at a fraction of the computational cost.

Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models

Chen, Y.-H. — Thu, 20 Aug 2009 10:00:44 PDT

A semiparametric transformation model comprises a parametric component for covariate effects and a nonparametric component for the baseline hazard/intensity. The Breslow-type estimator has been proposed for estimating the nonparametric component in some inefficient estimation procedures. We show that introducing weights into this estimator leads to nonparametric maximum likelihood estimation, with the weights depending on the martingale residuals. The weighted Breslow-type estimator suggests an iterative reweighting algorithm for nonparametric maximum likelihood estimation, which can be implemented by a weighted variant of the existing algorithms for inefficient estimation, and can be computationally more efficient than an em-type algorithm. The weighting idea is further extended to semiparametric transformation models with mismeasured covariates.

Pseudo-partial likelihood for proportional hazards models with biased-sampling data

Tsai, W. Y. — Thu, 20 Aug 2009 10:00:44 PDT

We obtain a pseudo-partial likelihood for proportional hazards models with biased-sampling data by embedding the biased-sampling data into left-truncated data. The log pseudo-partial likelihood of the biased-sampling data is the expectation of the log partial likelihood of the left-truncated data conditioned on the observed data. In addition, asymptotic properties of the estimator that maximize the pseudo-partial likelihood are derived. Applications to length-biased data, biased samples with right censoring and proportional hazards models with missing covariates are discussed.

Pseudo-partial likelihood estimators for the Cox regression model with missing covariates

Luo, X., Tsai, W. Y., Xu, Q. — Thu, 20 Aug 2009 10:00:44 PDT

By embedding the missing covariate data into a left-truncated and right-censored survival model, we propose a new class of weighted estimating functions for the Cox regression model with missing covariates. The resulting estimators, called the pseudo-partial likelihood estimators, are shown to be consistent and asymptotically normal. A simulation study demonstrates that, compared with the popular inverse-probability weighted estimators, the new estimators perform better when the observation probability is small and improve efficiency of estimating the missing covariate effects. Application to a practical example is reported.

Approximating the {alpha}-permanent

Kou, S. C., McCullagh, P. — Thu, 20 Aug 2009 10:00:44 PDT

The standard matrix permanent is the solution to a number of combinatorial and graph-theoretic problems, and the -weighted permanent is the density function for a class of Cox processes called boson processes. The exact computation of the ordinary permanent is known to be #P-complete, and the same appears to be the case for the -permanent for most values of . At present, the lack of a satisfactory algorithm for approximating the -permanent is a formidable obstacle to the use of boson processes in applied work. This paper proposes an importance-sampling estimator using nonuniform random permutations generated in a cycle format. Empirical investigation reveals that the estimator works well for the sorts of matrices that arise in point-process applications, involving up to a few hundred points. We conclude with a numerical illustration of the Bayes estimate of the intensity function of a boson point process, which is a ratio of -permanents.

Markov models for accumulating mutations

Beerenwinkel, N., Sullivant, S. — Thu, 20 Aug 2009 10:00:44 PDT

We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous-time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The partial order encodes constraints on the order in which mutations can fixate in the population, shedding light on the mutational pathways underlying the evolutionary process. We study a censored version of the model and derive equations for an em algorithm to perform maximum likelihood estimation of the model parameters. We also show how to select the maximum likelihood partially ordered set. The model is applied to genetic data from cancer cells and from drug resistant human immunodeficiency viruses, indicating implications for diagnosis and treatment.

Gaussian process emulation of dynamic computer codes

Conti, S., Gosling, J. P., Oakley, J. E., O'Hagan, A. — Thu, 20 Aug 2009 10:00:44 PDT

Computer codes are used in scientific research to study and predict the behaviour of complex systems. Their run times often make uncertainty and sensitivity analyses impractical because of the thousands of runs that are conventionally required, so efficient techniques have been developed based on a statistical representation of the code. The approach is less straightforward for dynamic codes, which represent time-evolving systems. We develop a novel iterative system to build a statistical model of dynamic computer codes, which is demonstrated on a rainfall-runoff simulator.

Optimal repeated measurement designs for a model with partial interactions

Druilhet, P., Tinsson, W. — Thu, 20 Aug 2009 10:00:44 PDT

We consider crossover designs for a model with partial interactions. In this model, the carryover effect depends on whether the treatment is preceded by itself or not. When the aim of the experiment is to study the total effects corresponding to a single treatment, we obtain approximate optimal symmetric designs, within the competing class of circular designs, by generalizing the method introduced by Kushner (1997) and Kunert & Martin (2000). This generalization places the method proposed by Bailey & Druilhet (2004) into Kushner's context. The optimal designs obtained are not binary, as in Kunert & Martin (2000). We also propose efficient designs generated by only one sequence.

Use of functionals in linearization and composite estimation with application to two-sample survey data

Goga, C., Deville, J.-C., Ruiz-Gazen, A. — Thu, 20 Aug 2009 10:00:44 PDT

An important problem associated with two-sample surveys is the estimation of nonlinear functions of finite population totals such as ratios, correlation coefficients or measures of income inequality. Computation and estimation of the variance of such complex statistics are made more difficult by the existence of overlapping units. In one-sample surveys, the linearization method based on the influence function approach is a powerful tool for variance estimation. We introduce a two-sample linearization technique that can be viewed as a generalization of the one-sample influence function approach. Our technique is based on expressing the parameters of interest as multivariate functionals of finite and discrete measures and then using partial influence functions to compute the linearized variables. Under broad assumptions, the asymptotic variance of the substitution estimator, derived from Deville (1999), is shown to be the variance of a weighted sum of the linearized variables. The paper then focuses on a general class of composite substitution estimators, and from this class the optimal estimator for minimizing the asymptotic variance is obtained. The efficiency of the optimal composite estimator is demonstrated through an empirical study.

Effects of data dimension on empirical likelihood

Chen, S. X., Peng, L., Qin, Y.-L. — Thu, 20 Aug 2009 10:00:44 PDT

We evaluate the effects of data dimension on the asymptotic normality of the empirical likelihood ratio for high-dimensional data under a general multivariate model. Data dimension and dependence among components of the multivariate random vector affect the empirical likelihood directly through the trace and the eigenvalues of the covariance matrix. The growth rates to infinity we obtain for the data dimension improve the rates of Hjort et al. (2008).

Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data

Cao, W., Tsiatis, A. A., Davidian, M. — Thu, 20 Aug 2009 10:00:44 PDT

Considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data, which involve models for both the propensity score and the regression of outcome on covariates. The usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations. We propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods, even with some estimated propensity scores close to zero.

A negative binomial model for time series of counts

Davis, R. A., Wu, R. — Thu, 20 Aug 2009 10:00:44 PDT

We study generalized linear models for time series of counts, where serial dependence is introduced through a dependent latent process in the link function. Conditional on the covariates and the latent process, the observation is modelled by a negative binomial distribution. To estimate the regression coefficients, we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed. We show the consistency and asymptotic normality of the generalized linear model estimator when the latent process is a stationary strongly mixing process. We extend the asymptotic results to generalized linear models for time series, where the observation variable, conditional on covariates and a latent process, is assumed to have a distribution from a one-parameter exponential family. Thus, we unify in a common framework the results for Poisson log-linear regression models of Davis et al. (2000), negative binomial logit regression models and other similarly specified generalized linear models.

A Student t-mixture autoregressive model with applications to heavy-tailed financial data

Wong, C. S., Chan, W. S., Kam, P. L. — Thu, 20 Aug 2009 10:00:44 PDT

We introduce the class of Student t-mixture autoregressive models, which is promising for financial time series modelling. The model is able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time varied from short-tailed to long-tailed, or from unimodal to multimodal. The use of t-distributed errors in each component of the model allows conditional leptokurtic distributions that account for the commonly observed excess unconditional kurtosis in financial data. Methods of parameter estimation and model selection are given. Finally, the proposed modelling procedure is illustrated through a real example.

Nonparametric Bayes local partition models for random effects

Dunson, D. B. — Wed, 20 May 2009 14:29:56 PDT

This paper focuses on the problem of choosing a prior for an unknown random effects distribution within a Bayesian hierarchical model. The goal is to obtain a sparse representation by allowing a combination of global and local borrowing of information. A local partition process prior is proposed, which induces dependent local clustering. Subjects can be clustered together for a subset of their parameters, and one learns about similarities between subjects increasingly as parameters are added. Some basic properties are described, including simple two-parameter expressions for marginal and conditional clustering probabilities. A slice sampler is developed which bypasses the need to approximate the countably infinite random measure in performing posterior computation. The methods are illustrated using simulation examples, and an application to hormone trajectory data.

Mixtures of Polya trees for flexible spatial frailty survival modelling

Zhao, L., Hanson, T. E., Carlin, B. P. — Wed, 20 May 2009 14:29:56 PDT

Mixtures of Polya trees offer a very flexible nonparametric approach for modelling time-to-event data. Many such settings also feature spatial association that requires further sophistication, either at the point level or at the lattice level. In this paper, we combine these two aspects within three competing survival models, obtaining a data analytic approach that remains computationally feasible in a fully hierarchical Bayesian framework using Markov chain Monte Carlo methods. We illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the Surveillance, Epidemiology and End Results program of the National Cancer Institute. Our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions, ignore spatial association or both.

Gamma frailty transformation models for multivariate survival times

Zeng, D., Chen, Q., Ibrahim, J. G. — Wed, 20 May 2009 14:29:57 PDT

We propose a class of transformation models for multivariate failure times. The class of transformation models generalize the usual gamma frailty model and yields a marginally linear transformation model for each failure time. Nonparametric maximum likelihood estimation is used for inference. The maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal, and their asymptotic variances attain the semiparametric efficiency bound. Simulation studies show that the proposed estimation procedure provides asymptotically efficient estimates and yields good inferential properties for small sample sizes. The method is illustrated using data from a cardiovascular study.

Generalized method of moments estimation for linear regression with clustered failure time data

Li, H., Yin, G. — Wed, 20 May 2009 14:29:57 PDT

We propose a generalized method of moments approach to the accelerated failure time model with correlated survival data. We study the semiparametric rank estimator using martingale-based moments. We circumvent direct estimation of correlation parameters by concatenating the moments and minimizing a quadratic objective function. We establish the consistency and asymptotic normality of the parameter estimators, and derive the limiting distribution of the objective function. We carry out simulation studies to examine the finite-sample properties of the method, and demonstrate its substantial efficiency gain over the conventional method. Finally, we illustrate the new proposal with an example from a diabetic retinopathy study.

Hierarchically penalized Cox regression with grouped variables

Wang, S., Nan, B., Zhu, N., Zhu, J. — Wed, 20 May 2009 14:29:57 PDT

In many biological and other scientific applications, predictors are often naturally grouped. For example, in biological applications, assayed genes or proteins are grouped by biological roles or biological pathways. When studying the dependence of survival outcome on these grouped predictors, it is desirable to select variables at both the group level and the within-group level. In this article, we develop a new method to address the group variable selection problem in the Cox proportional hazards model. Our method not only effectively removes unimportant groups, but also maintains the flexibility of selecting variables within the identified groups. We also show that the new method offers the potential for achieving the asymptotic oracle property.

A generalized Dantzig selector with shrinkage tuning

James, G. M., Radchenko, P. — Wed, 20 May 2009 14:29:57 PDT

The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L₁ penalty to shrink the regression coefficients towards zero, in a similar fashion to the lasso. While both the lasso and Dantzig selector potentially do a good job of selecting the correct variables, they tend to overshrink the final coefficients. This results in an unfortunate trade-off. One can either select a high shrinkage tuning parameter that produces an accurate model but poor coefficient estimates or a low shrinkage parameter that produces more accurate coefficients but includes many irrelevant variables. We extend the Dantzig selector to fit generalized linear models while eliminating overshrinkage of the coefficient estimates, and develop a computationally efficient algorithm, similar in nature to least angle regression, to compute the entire path of coefficient estimates. A simulation study illustrates the advantages of our approach relative to others. We apply the methodology to two datasets.

A group bridge approach for variable selection

Huang, J., Ma, S., Xie, H., Zhang, C.-H. — Wed, 20 May 2009 14:29:57 PDT

In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The existing methods, including the lasso and group lasso, are designed for either variable selection or group selection, but not for both. We propose a group bridge approach that is capable of simultaneous selection at both the group and within-group individual variable levels. The proposed approach is a penalized regularization method that uses a specially designed group bridge penalty. It has the oracle group selection property, in that it can correctly select important groups with probability converging to one. In contrast, the group lasso and group least angle regression methods in general do not possess such an oracle property in group selection. Simulation studies indicate that the group bridge has superior performance in group and individual variable selection relative to several existing methods.

Covariate-adjusted generalized linear models

Senturk, D., Muller, H.-G. — Wed, 20 May 2009 14:29:57 PDT

We propose covariate adjustment methodology for a situation where one wishes to study the dependence of a generalized response on predictors while both predictors and response are distorted by an observable covariate. The distorting covariate is thought of as a size measurement that affects predictors in a multiplicative fashion. The generalized response is modelled by means of a random threshold, where the subject-specific thresholds are affected by a multiplicative factor that is a function of the distorting covariate. While the various factors are modelled as smooth unknown functions of the distorting covariate, the underlying relationship between response and covariates is assumed to be governed by a generalized linear model with a known link function. This model provides an extension of a covariate-adjusted regression approach to the case of a generalized linear model. We demonstrate that this contamination model leads to a semiparametric varying-coefficient model. Numerical implementation is straightforward by combining binning, quasilikelihood, and smoothing steps. The asymptotic distribution of the proposed estimators for the regression coefficients of the latent generalized linear model is derived by means of a martingale central limit theorem. Combining this result with consistent estimators for the asymptotic variance makes it then possible to obtain asymptotic inference for the targeted parameters. Both real and simulated data are used in illustrating the proposed methodology.

Adjusting for covariate effects on classification accuracy using the covariate-adjusted receiver operating characteristic curve

Janes, H., Pepe, M. S. — Wed, 20 May 2009 14:29:57 PDT

Recent scientific and technological innovations have produced an abundance of potential markers that are being investigated for their use in disease screening and diagnosis. In evaluating these markers, it is often necessary to account for covariates associated with the marker of interest. Covariates may include subject characteristics, expertise of the test operator, test procedures or aspects of specimen handling. In this paper, we propose the covariate-adjusted receiver operating characteristic curve, a measure of covariate-adjusted classification accuracy. Nonparametric and semiparametric estimators are proposed, asymptotic distribution theory is provided and finite sample performance is investigated. For illustration we characterize the age-adjusted discriminatory accuracy of prostate-specific antigen as a biomarker for prostate cancer.

Nonparametric additive regression for repeatedly measured data

Carroll, R. J., Maity, A., Mammen, E., Yu, K. — Wed, 20 May 2009 14:29:57 PDT

We develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems. Our methodology easily copes with various settings, such as when some covariates are the same over repeated response measurements. We allow for a working covariance matrix for the regression errors, showing that our method is most efficient when the correct covariance matrix is used. The component functions achieve the known asymptotic variance lower bound for the scalar argument case. Smooth backfitting also leads directly to design-independent biases in the local linear case. Simulations show our estimator has smaller variance than the usual kernel estimator. This is also illustrated by an example from nutritional epidemiology.

Optimal testing of multiple hypotheses with common effect direction

Bittman, R. M., Romano, J. P., Vallarino, C., Wolf, M. — Wed, 20 May 2009 14:29:57 PDT

We present a theoretical basis for testing related endpoints. Typically, it is known how to construct tests of the individual hypotheses, but not how to combine them into a multiple test procedure that controls the familywise error rate. Using the closure method, we emphasize the role of consonant procedures, from an interpretive as well as a theoretical viewpoint. Surprisingly, even if each intersection test has an optimality property, the overall procedure obtained by applying closure to these tests may be inadmissible. We introduce a new procedure, which is consonant and has a maximin property under the normal model. The results are then applied to PROactive, a clinical trial designed to investigate the effectiveness of a glucose-lowering drug on macrovascular outcomes among patients with type 2 diabetes.

Non-finite Fisher information and homogeneity: an EM approach

Li, P., Chen, J., Marriott, P. — Wed, 20 May 2009 14:29:57 PDT

Even simple examples of finite mixture models can fail to fulfil the regularity conditions that are routinely assumed in standard parametric inference problems. Many methods have been investigated for testing for homogeneity in finite mixture models, for example, but all rely on regularity conditions including the finiteness of the Fisher information and the space of the mixing parameter being a compact subset of some Euclidean space. Very simple examples where such assumptions fail include mixtures of two geometric distributions and two exponential distributions, and, more generally, mixture models in scale distribution families. To overcome these difficulties, we propose and study an em-test statistic, which has a simple limiting distribution for examples in this paper. Simulations show that the em-test has accurate Type I errors and is more efficient than existing methods when they are applicable. A real example is included.

Double block bootstrap confidence intervals for dependent data

Lee, S. M. S., Lai, P. Y. — Wed, 20 May 2009 14:29:57 PDT

The block bootstrap confidence interval for dependent data can outperform the conventional normal approximation only with nontrivial studentization which, in the case of complicated statistics, calls for specialist treatment and often results in unstable endpoints. We propose two double block bootstrap approaches for improving the accuracy of the block bootstrap confidence interval under very general conditions. The first approach calibrates the nominal coverage level and the second calculates studentizing factors directly from a block bootstrap series without the need for nontrivial analytical treatment. We prove that the two approaches reduce the coverage error of the block bootstrap interval by an order of magnitude with simple tuning of block lengths at the two block bootstrapping levels. Empirical properties of the procedures are investigated by simulations and application to an econometric time series.

Marginal analysis of panel counts through estimating functions

Hu, X. J., Lagakos, S. W., Lockhart, R. A. — Wed, 20 May 2009 14:29:57 PDT

We develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations, using two types of self-consistent estimating equations. The first is derived from the likelihood studied by Wellner & Zhang (2000), assuming a Poisson counting process. It gives a nondecreasing estimator, which equals the nonparametric maximum likelihood estimator of Wellner & Zhang and is consistent without the Poisson assumption. Motivated by the construction of parametric generalized estimating equations, the second type is a set of data-adaptive quasi-score functions, which are likelihood estimating functions under a mixed-Poisson assumption. We evaluate the procedures using simulation, and illustrate them with the data from a bladder cancer study.

Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models

Lohr, S. L., Rao, J. N. K. — Wed, 20 May 2009 14:29:57 PDT

Empirical Bayes predictors of small area parameters of interest are often obtained under a linear mixed model for continuous response data or a generalized linear mixed model for binary responses or count data. However, estimation of the unconditional mean squared error of prediction is complicated, particularly for a nonlinear mixed model. Jiang et al. (2002) proposed a jackknife method for estimating the unconditional mean squared error and showed that the resulting estimator is nearly unbiased. The leading term of this estimator does not depend on the area-specific responses in the nonlinear case, whereas the posterior variance of the small area parameter given the model parameters is area-specific. Rao (2003) proposed an alternative method that leads to a computationally simpler jackknife estimator with an area-specific leading term. We show that a modification of Rao's method leads to a nearly unbiased area-specific jackknife estimator, which is also nearly unbiased for the conditional mean squared error given the area-specific responses. We examine the relative performances of the jackknife estimators, conditionally as well as unconditionally, in a simulation study, and apply the proposed method to estimate small area mean squared errors in disease mapping problems.

Scale adjustments for classifiers in high-dimensional, low sample size settings

Chan, Y.-B., Hall, P. — Wed, 20 May 2009 14:29:57 PDT

Distance-based classifiers are generally considered to be effective at discriminating between populations that differ in location. Indeed, nearest-neighbour methods and the support vector machine are frequently used in very high-dimensional problems involving gene expression data, where it is believed that elevated levels of expression convey much of the information for classification. However, one problem inherent to distance-based classifiers is that scale differences can mask location differences. In consequence, such classifiers can have poor performance if the information for classification accumulates through a large number of relatively small location differences in data components, rather than via large differences. In this paper, we show that a simple adjustment for scale, applicable to a variety of distance-based classifiers, can remedy the problem. For some classifiers, such as those based on the support vector machine or the centroid method, scale corrections are important primarily in the case of small training-sample sizes. However, for other classifiers, including those based on nearest-neighbour and average-distance methods, scale adjustments are helpful more generally.

Saddlepoint approximation for mixture models

Davison, A. C., Mastropietro, D. — Wed, 20 May 2009 14:29:57 PDT

Two-component mixture distributions with one component a point mass and the other a continuous density may be used as priors for Bayesian inference when sparse representation of an underlying signal is required. We show how saddlepoint approximation in such models can yield highly accurate quantiles for posterior distributions, and illustrate this numerically, using wavelet regression with point mass/Laplace and point mass/normal prior distributions.

Some results on D-optimal designs for nonlinear models with applications

Li, G., Majumdar, D. — Wed, 20 May 2009 14:29:57 PDT

Sufficient conditions are established for the locally D$-optimal design for a nonlinear model to have a minimal number of support points. The conditions are applied to obtain locally D-optimal designs for a one-compartment pharmacokinetic model and a Poisson regression model.

Dimension reduction in time series and the dynamic factor model

Pena, D. — Wed, 20 May 2009 14:29:57 PDT

This note shows that the dimension reduction method proposed by Li & Shedden (2002) is equivalent to the dynamic factor model introduced by Peña & Box (1987).

Modelling pairwise dependence of maxima in space

Naveau, P., Guillou, A., Cooley, D., Diebolt, J. — Fri, 13 Feb 2009 13:35:00 PST

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.

Efficient nonparametric estimation of causal effects in randomized trials with noncompliance

Cheng, J., Small, D. S., Tan, Z., Ten Have, T. R. — Fri, 13 Feb 2009 13:35:01 PST

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.

Partial and latent ignorability in missing-data problems

Harel, O., Schafer, J. L. — Fri, 13 Feb 2009 13:35:01 PST

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.

Orthogonal and nearly orthogonal designs for computer experiments

Bingham, D., Sitter, R. R., Tang, B. — Fri, 13 Feb 2009 13:35:01 PST

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.

D-optimal design of split-split-plot experiments

Jones, B., Goos, P. — Fri, 13 Feb 2009 13:35:01 PST

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.

Optimal two-level regular fractional factorial block and split-plot designs

Cheng, C.-S., Tsai, P.-W. — Fri, 13 Feb 2009 13:35:01 PST

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.

Bayesian-inspired minimum aberration two- and four-level designs

Joseph, V. R., AI, M., Wu, C. F. J. — Fri, 13 Feb 2009 13:35:01 PST

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.

Confidence intervals for spectral mean and ratio statistics

Shao, X. — Fri, 13 Feb 2009 13:35:01 PST

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.

Tapered empirical likelihood for time series data in time and frequency domains

Nordman, D. J. — Fri, 13 Feb 2009 13:35:01 PST

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.

Model checking in regression via dimension reduction

Xia, Y. — Fri, 13 Feb 2009 13:35:01 PST

Lack-of-fit checking for parametric and semiparametric models is essential in reducing misspecification. The efficiency of most existing model-checking methods drops rapidly as the dimension of the covariates increases. We propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern. Consistency of the method is proved for parametric and semiparametric regression models. A bootstrap implementation is also discussed. Simulation comparisons with several existing methods are made, suggesting that the proposed methods are more efficient than the existing methods when the dimension increases. Air pollution data from Chicago are used to illustrate the procedure.

Bayesian nonparametric functional data analysis through density estimation

Rodriguez, A., Dunson, D. B., Gelfand, A. E. — Fri, 13 Feb 2009 13:35:01 PST

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.

Wilcoxon-type generalized Bayesian information criterion

Wang, L. — Fri, 13 Feb 2009 13:35:01 PST

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 L₂ risk. On the other hand, when the data are normally distributed, both criteria have similar L₂ 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.

Reducing variability of crossvalidation for smoothing-parameter choice

Hall, P., Robinson, A. P. — Fri, 13 Feb 2009 13:35:01 PST

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%.

Dealing with limited overlap in estimation of average treatment effects

Crump, R. K., Hotz, V. J., Imbens, G. W., Mitnik, O. A. — Fri, 13 Feb 2009 13:35:01 PST

Estimation of average treatment effects under unconfounded or ignorable treatment assignment is often hampered by lack of overlap in the covariate distributions between treatment groups. This lack of overlap can lead to imprecise estimates, and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used ad hoc methods for trimming the sample. We develop a systematic approach to addressing lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely. Under some conditions, the optimal selection rules depend solely on the propensity score. For a wide range of distributions, a good approximation to the optimal rule is provided by the simple rule of thumb to discard all units with estimated propensity scores outside the range [0.1,0.9].

On fuzzy familywise error rate and false discovery rate procedures for discrete distributions

Kulinskaya, E., Lewin, A. — Fri, 13 Feb 2009 13:35:01 PST

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.

Fast block variance estimation procedures for inhomogeneous spatial point processes

Guan, Y. — Fri, 13 Feb 2009 13:35:01 PST

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.

A note on semiparametric efficient inference for two-stage outcome-dependent sampling with a continuous outcome

Song, R., Zhou, H., Kosorok, M. R. — Fri, 13 Feb 2009 13:35:02 PST

Outcome-dependent sampling designs have been shown to be a cost-effective way to enhance study efficiency. We show that the outcome-dependent sampling design with a continuous outcome can be viewed as an extension of the two-stage case-control designs to the continuous-outcome case. We further show that the two-stage outcome-dependent sampling has a natural link with the missing-data and biased-sampling frameworks. Through the use of semiparametric inference and missing-data techniques, we show that a certain semiparametric maximum-likelihood estimator is computationally convenient and achieves the semiparametric efficient information bound. We demonstrate this both theoretically and through simulation.

A note on profile likelihood for exponential tilt mixture models

Tan, Z. — Fri, 13 Feb 2009 13:35:02 PST

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.

A note on cause-specific residual life

Jeong, J.-H., Fine, J. P. — Fri, 13 Feb 2009 13:35:02 PST

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.

Construction of orthogonal and nearly orthogonal Latin hypercubes

Lin, C. D., Mukerjee, R., Tang, B. — Fri, 13 Feb 2009 13:35:02 PST

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.

A note on time-ordered classification

He, H. — Fri, 13 Feb 2009 13:35:02 PST