Biometrika - current issue

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.