Student-t censored regression model: properties and inference

In statistical analysis, particularly in econometrics, it is usual to consider regression models where the dependent variable is censored (limited). In particular, a censoring scheme to the left of zero is considered here. In this article, an extension of the classical normal censored model is developed by considering independent disturbances with identical Student-t distribution. In the context of maximum likelihood estimation, an expression for the expected information matrix is provided, and an efficient EM-type algorithm for the estimation of the model parameters is developed. In order to know what type of variables affect the income of housewives, the results and methods are applied to a real data set. A brief review on the normal censored regression model or Tobit model is also presented.     

Empirical Non-Parametric Control Charts: Estimation Effects and Corrections

Owing to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and non-normality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a large model is inadequate and nothing remains but to consider non- parametric charts. In principle, these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage that seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyse under what conditions non-parametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes that are markedly less huge (but still larger than the customary range). These corrections serve to control the behaviour during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection will clearly be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.     

The ℓ1 oblique procrustes problem

In this paper, we reconsider the well-known oblique Procrustes problem where the usual least-squares objective function is replaced by a more robust discrepancy measure, based on the ₁ norm or smooth approximations of it.We propose two approaches to the solution of this problem. One approach is based on convex analysis and uses the structure of the problem to permit a solution to the ₁ norm problem. An alternative approach is to smooth the problem by working with smooth approximations to the ₁ norm, and this leads to a solution process based on the solution of ordinary differential equations on manifolds. The general weighted Procrustes problem (both orthogonal and oblique) can also be solved by the latter approach. Numerical examples to illustrate the algorithms which have been developed are reported and analyzed.     

Analysis of longitudinal multiple-source binary data using generalized estimating equations

Summary.  We present a multivariate logistic regression model for the joint analysis of longitudinal multiple-source binary data. Longitudinal multiple-source binary data arise when repeated binary measurements are obtained from two or more sources, with each source providing a measure of the same underlying variable. Since the number of responses on each subject is relatively large, the empirical variance estimator performs poorly and cannot be relied on in this setting. Two methods for obtaining a parsimonious within-subject association structure are considered. An additional complication arises with estimation, since maximum likelihood estimation may not be feasible without making unrealistically strong assumptions about third- and higher order moments. To circumvent this, we propose the use of a generalized estimating equations approach. Finally, we present an analysis of multiple-informant data obtained longitudinally from a psychiatric interventional trial that motivated the model developed in the paper.     

Bayesian prediction for progressively censored data from the Burr model

Received: August 14, 2000; revised version: April 23, 2001     

Bayes model averaging with selection of regressors

Summary. When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly reduced predictor space. This can greatly aid the interpretation of the model. It also reduces the cost if measured variables have costs. The development here uses decision theory in the context of the multivariate general linear model. In passing, this reduced predictor space Bayes model averaging is contrasted with single-model approximations. A fast algorithm for updating regressions in the Markov chain Monte Carlo searches for posterior inference is developed, allowing many more variables than observations to be contemplated. We discuss the merits of absolute rather than proportionate shrinkage in regression, especially when there are more variables than observations. The methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution.     

Perfect samplers for mixtures of distributions

Summary. We consider the construction of perfect samplers for posterior distributions associated with mixtures of exponential families and conjugate priors, starting with a perfect slice sampler in the spirit of Mira and co-workers. The methods rely on a marginalization akin to Rao–Blackwellization and illustrate the duality principle of Diebolt and Robert. A first approximation embeds the finite support distribution on the latent variables within a continuous support distribution that is easier to simulate by slice sampling, but we later demonstrate that the approximation can be very poor. We conclude by showing that an alternative perfect sampler based on a single backward chain can be constructed. This alternative can handle much larger sample sizes than the slice sampler first proposed.     

Random effects and shrinkage estimation in capture-recapture models

We discuss the analysis of random effects in capture-recapture models, and outline Bayesian and frequentists approaches to their analysis. Under a normal model, random effects estimators derived from Bayesian or frequentist considerations have a common form as shrinkage estimators. We discuss some of the difficulties of analysing random effects using traditional methods, and argue that a Bayesian formulation provides a rigorous framework for dealing with these difficulties. In capture-recapture models, random effects may provide a parsimonious compromise between constant and completely time-dependent models for the parameters (e.g. survival probability). We consider application of random effects to band-recovery models, although the principles apply to more general situations, such as Cormack-Jolly-Seber models. We illustrate these ideas using a commonly analysed band recovery data set.     

The use of resighting data to estimate the rate of population growth of the snail kite in Florida

The rate of population growth ( u ) is an important demographic parameter used to assess the viability of a population and to develop management and conservation agendas. We examined the use of resighting data to estimate u for the snail kite population in Florida from 1997-2000. The analyses consisted of (1) a robust design approach that derives an estimate of u from estimates of population size and (2) the Pradel (1996) temporal symmetry (TSM) approach that directly estimates u using an open-population capture-recapture model. Besides resighting data, both approaches required information on the number of unmarked individuals that were sighted during the sampling periods. The point estimates of u differed between the robust design and TSM approaches, but the 95% confidence intervals overlapped substantially. We believe the differences may be the result of sparse data and do not indicate the inappropriateness of either modelling technique. We focused on the results of the robust design because this approach provided estimates for all study years. Variation among these estimates was smaller than levels of variation among ad hoc estimates based on previously reported index statistics. We recommend that u of snail kites be estimated using capture-resighting methods rather than ad hoc counts.     

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