Biometrika - current issue

Sinh-arcsinh distributions

Jones, M. C., Pewsey, A. — Tue, 24 Nov 2009 02:59:10 PST

We introduce the sinh-arcsinh transformation and hence, by applying it to a generating distribution with no parameters other than location and scale, usually the normal, a new family of sinh-arcsinh distributions. This four-parameter family has symmetric and skewed members and allows for tailweights that are both heavier and lighter than those of the generating distribution. The central place of the normal distribution in this family affords likelihood ratio tests of normality that are superior to the state-of-the-art in normality testing because of the range of alternatives against which they are very powerful. Likelihood ratio tests of symmetry are also available and are very successful. Three-parameter symmetric and asymmetric subfamilies of the full family are also of interest. Heavy-tailed symmetric sinh-arcsinh distributions behave like Johnson S_U distributions, while their light-tailed counterparts behave like sinh-normal distributions, the sinh-arcsinh family allowing a seamless transition between the two, via the normal, controlled by a single parameter. The sinh-arcsinh family is very tractable and many properties are explored. Likelihood inference is pursued, including an attractive reparameterization. Illustrative examples are given. A multivariate version is considered. Options and extensions are discussed.

A new look at time series of counts

Cui, Y., Lund, R. — Tue, 24 Nov 2009 02:59:10 PST

This paper proposes a simple new model for stationary time series of integer counts. Previous work has focused on thinning methods and classical time series autoregressive moving-average difference equations; in contrast, our methods use a renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such processes, stationary series with binomial, Poisson, geometric or any other discrete marginal distribution can be readily constructed. The model class proposed is parsimonious, non-Markov and readily generates series with either short- or long-memory autocovariances. The model can be fitted with linear prediction techniques for stationary series. As an example, a stationary series with binomial marginal distributions is fitted to the number of rainy days in 210 consecutive weeks at Key West, Florida.

Bias reduction in exponential family nonlinear models

Kosmidis, I., Firth, D. — Tue, 24 Nov 2009 02:59:10 PST

In Firth (1993, Biometrika) it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector, and that in canonical-link generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data. Here a more general family of bias-reducing adjustments is developed for a broad class of univariate and multivariate generalized nonlinear models. The resulting formulae for the adjusted score vector are computationally convenient, and in univariate models they directly suggest implementation through an iterative scheme of data adjustment. For generalized linear models a necessary and sufficient condition is given for the existence of a penalized likelihood interpretation of the method. An illustrative application to the Goodman row-column association model shows how the computational simplicity and statistical benefits of bias reduction extend beyond generalized linear models.

Inference on population size in binomial detectability models

Fewster, R. M., Jupp, P. E. — Tue, 24 Nov 2009 02:59:10 PST

Many models for biological populations, including simple mark-recapture models and distance sampling models, involve a binomially distributed number, n, of observations x₁, ..., x_n on members of a population of size N. Two popular estimators of (N, ), where is a vector parameter, are the maximum likelihood estimator and the conditional maximum likelihood estimator based on the conditional distribution of x₁, ..., x_n given n. We derive the large-N asymptotic distributions of and , and give formulae for the biases of and . We show that the difference is, remarkably, of order 1 and we give a simple formula for the leading part of this difference. Simulations indicate that in many cases this formula is very accurate and that confidence intervals based on the asymptotic distribution have excellent coverage. An extension to product-binomial models is given.

Bayesian analysis of matrix normal graphical models

Wang, H., West, M. — Tue, 24 Nov 2009 02:59:10 PST

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Extensions to matrix-variate time series embed matrix normal graphs in dynamic models. Examples highlight questions of graphical model uncertainty, search and comparison in matrix data contexts. These models may be applied in a number of areas of multivariate analysis, time series and also spatial modelling.

Bayesian lasso regression

Hans, C. — Tue, 24 Nov 2009 02:59:10 PST

The lasso estimate for linear regression corresponds to a posterior mode when independent, double-exponential prior distributions are placed on the regression coefficients. This paper introduces new aspects of the broader Bayesian treatment of lasso regression. A direct characterization of the regression coefficients’ posterior distribution is provided, and computation and inference under this characterization is shown to be straightforward. Emphasis is placed on point estimation using the posterior mean, which facilitates prediction of future observations via the posterior predictive distribution. It is shown that the standard lasso prediction method does not necessarily agree with model-based, Bayesian predictions. A new Gibbs sampler for Bayesian lasso regression is introduced.

Generalized fiducial inference for wavelet regression

Hannig, J., Lee, T. C. M. — Tue, 24 Nov 2009 02:59:10 PST

We apply Fisher’s fiducial idea to wavelet regression, first developing a general methodology for handling model selection problems within the fiducial framework. We propose fiducial-based methods for wavelet curve estimation and the construction of pointwise confidence intervals. We show that these confidence intervals have asymptotically correct coverage. Simulations demonstrate that they possess promising empirical properties.

Nonparametric estimation of the probability of illness in the illness-death model under cross-sectional sampling

Mandel, M., Fluss, R. — Tue, 24 Nov 2009 02:59:10 PST

Cross-sectional sampling is an attractive design that saves resources but results in biased data. For proper inference, one should first discover the bias function and then weigh observations appropriately. We consider cross-sectioning of the illness-death model with the aim of estimating the probability of visiting the illness state before death. We develop simple consistent and asymptotically normal estimators under various assumptions on the model and data collection and, in particular, compare designs with and without a follow-up. These designs are common in surveillance of hospital acquired infections, but estimators currently in use do not properly correct the bias.

Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach

Luo, X., Tsai, W. Y. — Tue, 24 Nov 2009 02:59:10 PST

To estimate the lifetime distribution of right-censored length-biased data, we propose a pseudo-partial likelihood approach that allows us to derive two nonparametric estimators. With its closed-form estimators and explicit limiting variances, this approach retains the simplicity of conditional analysis, and has only a small efficiency loss compared with the unconditional analysis. Under some regularity conditions, we show that the two estimators are uniformly consistent and converge weakly to Gaussian processes. A simulation study demonstrates that the proposed estimators have satisfactory finite-sample performance. Application to an Alzheimer’s disease study is reported.

Marginal hazards model for case-cohort studies with multiple disease outcomes

Kang, S., Cai, J. — Tue, 24 Nov 2009 02:59:10 PST

Case-cohort study designs are widely used to reduce the cost of large cohort studies while achieving the same goals, especially when the disease rate is low. A key advantage of the case-cohort study design is its capacity to use the same subcohort for several diseases or for several subtypes of disease. In order to compare the effect of a risk factor on different types of diseases, times to different events need to be modelled simultaneously. Valid statistical methods that take the correlations among the outcomes from the same subject into account need to be developed. To this end, we consider marginal proportional hazards regression models for case-cohort studies with multiple disease outcomes. We also consider generalized case-cohort designs that do not require sampling all the cases, which is more realistic for multiple disease outcomes. We propose an estimating equation approach for parameter estimation with two different types of weights. Consistency and asymptotic normality of the proposed estimators are established. Large sample approximation works well in small samples in simulation studies. The proposed methods are applied to the Busselton Health Study.

Tests and confidence intervals for secondary endpoints in sequential clinical trials

Lai, T. L., Shih, M.-C., Su, Z. — Tue, 24 Nov 2009 02:59:10 PST

In a sequential clinical trial whose stopping rule depends on the primary endpoint, inference on secondary endpoints is an important long-standing problem. Ignoring the possibility of early stopping based on the primary endpoint may result in substantial bias. To address this problem, a commonly used approach is to develop bias correction by estimating the bias in the case of bivariate normal outcomes and appealing to joint asymptotic normality of the statistics associated with the primary and secondary endpoints. We propose herein a new approach that uses resampling and a novel ordering scheme in the sample space of sequential statistics observed up to a stopping time. This approach is shown to provide accurate inference in complex clinical trials, including time-sequential trials with survival endpoints and covariates.

A unified approach to linearization variance estimation from survey data after imputation for item nonresponse

Kim, J. K., Rao, J. N. K. — Tue, 24 Nov 2009 02:59:10 PST

Variance estimation after imputation is an important practical problem in survey sampling. When deterministic imputation or stochastic imputation is used, we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach. We provide some applications of the approach to regression imputation, fractional categorical imputation, multiple imputation and composite imputation. Results from a simulation study, under a factorial structure for the sampling, response and imputation mechanisms, show that the proposed linearization variance estimator performs well in terms of relative bias, assuming a missing at random response mechanism.

Some design properties of a rejective sampling procedure

Fuller, W. A. — Tue, 24 Nov 2009 02:59:10 PST

Occasionally, a selected probability sample may appear undesirable with respect to the available auxiliary information. In such a situation, the practitioner might consider rejecting the sample and selecting a new set of sample elements. We consider a procedure in which the probability sample is rejected unless the sample mean of an auxiliary vector is within a specified distance of the population mean. It is proven that the large sample mean and variance of the regression estimator for the rejective sample are the same as those of the regression estimator for the original selection procedure. Likewise, the usual estimator of variance for the regression estimator is appropriate for the rejective sample. In a Monte Carlo experiment, the large sample properties hold for relatively small samples and the Monte Carlo results are in agreement with the theoretical orders of approximation. The efficiency effect of the described rejective sampling is o(n_N^–1, where n_N is the expected sample size, but the effect can be important for particular samples. For example, rejective sampling can be used to eliminate those samples that give negative weights for the regression estimator.

Sliced space-filling designs

Qian, P. Z. G., Wu, C. F. J. — Tue, 24 Nov 2009 02:59:10 PST

We propose an approach to constructing a new type of design, a sliced space-filling design, intended for computer experiments with qualitative and quantitative factors. The approach starts with constructing a Latin hypercube design based on a special orthogonal array for the quantitative factors and then partitions the design into groups corresponding to different level combinations of the qualitative factors. The points in each group have good space-filling properties. Some illustrative examples are given.

Nested Latin hypercube designs

Qian, P. Z. G. — Tue, 24 Nov 2009 02:59:10 PST

We propose an approach to constructing nested Latin hypercube designs. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. A nested Latin hypercube design with two layers is defined to be a special Latin hypercube design that contains a smaller Latin hypercube design as a subset. Our method is easy to implement and can accommodate any number of factors. We also extend this method to construct nested Latin hypercube designs with more than two layers. Illustrative examples are given. Some statistical properties of the constructed designs are derived.

Construction of orthogonal Latin hypercube designs

Sun, F., Liu, M.-Q., Lin, D. K. J. — Tue, 24 Nov 2009 02:59:11 PST

Latin hypercube designs have found wide application. Such designs guarantee uniform samples for the marginal distribution of each input variable. We propose a method for constructing orthogonal Latin hypercube designs in which all the linear terms are orthogonal not only to each other, but also to the quadratic terms. This construction method is convenient and flexible, and the resulting designs can accommodate many more factors than can existing ones.

Maximum likelihood estimation using composite likelihoods for closed exponential families

Mardia, K. V., Kent, J. T., Hughes, G., Taylor, C. C. — Tue, 24 Nov 2009 02:59:11 PST

In certain multivariate problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions may be much more tractable. In this paper we investigate the use of composite likelihoods instead of the full likelihood. For closed exponential families, both are shown to be maximized by the same parameter values for any number of observations. Examples include log-linear models and multivariate normal models. In other cases the parameter estimate obtained by maximizing a composite likelihood can be viewed as an approximation to the full maximum likelihood estimate. An application is given to an example in directional data based on a bivariate von Mises distribution.

Adaptive approximate Bayesian computation

Beaumont, M. A., Cornuet, J.-M., Marin, J.-M., Robert, C. P. — Tue, 24 Nov 2009 02:59:11 PST

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappé et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

Semiparametric methods for evaluating risk prediction markers in case-control studies

Huang, Y., Pepe, M. S. — Tue, 24 Nov 2009 02:59:11 PST

The performance of a well-calibrated risk model for a binary disease outcome can be characterized by the population distribution of risk and displayed with the predictiveness curve. Better performance is characterized by a wider distribution of risk, since this corresponds to better risk stratification in the sense that more subjects are identified at low and high risk for the disease outcome. Although methods have been developed to estimate predictiveness curves from cohort studies, most studies to evaluate novel risk prediction markers employ case-control designs. Here we develop semiparametric methods that accommodate case-control data. The semiparametric methods are flexible, and naturally generalize methods previously developed for cohort data. Applications to prostate cancer risk prediction markers illustrate the methods.

A note on the variance of doubly-robust G-estimators

Moodie, E. E. M. — Tue, 24 Nov 2009 02:59:11 PST

A recursive variance calculation is derived for doubly-robust G-estimators for dynamic treatment regimes in a multi-interval setting. Treatment decision parameters are not assumed to be shared across treatment intervals; this independence of parameters permits sequential estimation of the G-estimators’ variance when G-estimation is performed in a sequential fashion. The recursive variance calculation is both natural and computationally feasible. This development can easily be adapted to other complex estimating procedures that require nuisance parameter estimation.

A note on automatic variable selection using smooth-threshold estimating equations

Ueki, M. — Tue, 24 Nov 2009 02:59:11 PST

This paper develops smooth-threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero. The resulting estimator enjoys the oracle property in the sense of Fan & Li (2001), even in estimators for which the covariance assumption of Wang & Leng (2007) is violated, such as the Buckley–James estimator. Furthermore, the estimator can be obtained without solving a convex optimization problem. A bic-type criterion for tuning parameter selection is also proposed. It is shown that the criterion achieves consistent model selection. A numerical study confirms the performance of the method.

A note on adaptive Bonferroni and Holm procedures under dependence

Guo, W. — Tue, 24 Nov 2009 02:59:11 PST

Hochberg & Benjamini (1990) first presented adaptive procedures for controlling familywise error rate. However, until now, it has not been proved that these procedures control the familywise error rate. We introduce a simplified version of Hochberg & Benjamini’s adaptive Bonferroni and Holm procedures. Assuming a conditional dependence model, we prove that the former procedure controls the familywise error rate in finite samples while the latter controls it approximately.

A note on a conjectured sharpness principle for probabilistic forecasting with calibration

Pal, S. — Tue, 24 Nov 2009 02:59:11 PST

This note proves a weak sharpness principle as conjectured by Gneiting et al. (2007) in connection with probabilistic forecasting subject to calibration constraints.

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

Li, H., Yin, G. — Tue, 24 Nov 2009 02:59:11 PST