Consider the problem of estimating the ratio of variances based on independent samples from two normal populations. Gelfand and Dey (1988) showed that, for unknown population means, the usual best multiple of the ratio of the two sample variances was no longer admissible under any quadratic loss. The estimators dominating the best multiple estimator were analogous to the estimators developed earlier by Stein (1964) andBrown (1968) in the one-sample problem of estimating a normal variance. All such estimators are non-smooth, and, hence, are inadmissible. The present paper develops some hierarchical Bayes estimators of the ratio of variances using priors similar to the ones given in Ghosh (1994). Some of these hierarchical Bayes estimators are shown to dominate the best multiple estimator. The method of proof involves a two-sample extension of the arguments of Kubokawa (1994) in the one-sample problem.
Stein and Haff's technique is used to obtain improved, estimators of the multinormal precision matrix under a loss introduced by Efron and Morris (1976). The technique is to obtain solutions to a certain differential inequality involving the eigenvalues of the sample covarianze matrix. A neu class of -improved estimators are obtained by solving the differential inequality.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.