Showing papers by "William E. Strawderman published in 1996"

Choice of hierarchical priors: admissibility in estimation of normal means

Abstract: In hierarchical Bayesian modeling of normal means, it is common to complete the prior specification by choosing a constant prior density for unmodeled hyperparameters (e.g., variances and highest-level means). This common practice often results in an inadequate overall prior, inadequate in the sense that estimators resulting from its use can be inadmissible under quadratic loss. In this paper, hierarchical priors for normal means are categorized in terms of admissibility and inadmissibility of resulting estimators for a quite general scenario. The Jeffreys prior for the hyper-variance and a shrinkage prior for the hypermeans are recommended as admissible alternatives. Incidental to this analysis is presentation of the conditions under which the (generally improper) priors result in proper posteriors.

A Bayesian growth and yield model for slash pine plantations

Abstract: We formulate a traditional growth and yield model as a Bayes model. We attempt to introduce as few new assumptions as possible. Zellner's Bayesian method of moments procedure is used, because the published model did not include any distributional assumptions. We generate predictive posterior samples for a number of stand variables using the Gibbs sampler. The means of the samples compare favorably with the predictions from the published model. In addition, our model delivers distributions of outcomes, from which it is easy to establish measures of uncertainty, such as highest posterior density regions.

Improving on truncated linear estimates of exponential and gamma scale parameters

Abstract: We consider the problem of estimating the scale parameter of an exponential or a gamma distribution under squared error loss when the scale parameter θ is known to be greater than some fixed value θ0. Natural estimators in this setting include truncated linear functions of the sufficient statistic. Such estimators are typically inadmissible, but explicit improvements seem difficult to find. Some are presented here. A particularly interesting finding is that estimators which are admissible in the untruncated problem which take values only in the interior of the truncated parameter space are found to be inadmissible for the truncated problem. Cet article aborde le probleme de I'estimation du parametre d'echelle θ d'une loi exponentielle ou gamma, dans le cas ou θ ≥ θ0 et ou I'on cherche a minimiser I'erreur quadratique moyenne. Dans ce contexte, les fonctions lineaires tronquees de la statistique exhaustive canonique sont des candidats naturels et bien qu'ils soient generalement inadmissibles, il est difficile d'expliciter de meilleurs estimateurs. C'est neanmoins ce qui est fait ici. Ceci permet entre autres d'etablir I'inadmissibilite de certains estimateurs dont la valeur est toujours superieure a θ0 et qui sont pourtant admissibles lorsqu'il n'existe aucune contrainte sur θ.

Evaluating Cumulated Research I: The Traditional Methods Inadequacy of

Abstract: Virtually all reviews of cumulated studies rely on statistical significance as a criterion for evaluating the reproducibility of the phenomenon under review. Despite its nearly universal application, that criterion is entirely inadequate: Its application is very likely to lead a reviewer to conclude that a phenomenon does not discriminate patients from controls when, in fact, it does do so. The reviewer is, paradoxically, more likely to draw this incorrect conclusion as more studies become available for review. It can lead a reviewer to conclude that one phenomenon is more discriminating than another when the opposite is actually true. Fortunately, procedures that do not distort the review process are available; some of these are briefly discussed.