Bayes Minimax Competitors of Preliminary Test Estimators in k Sample Problems

TL;DR

This paper develops Bayesian estimators for multivariate normal means that improve upon traditional preliminary test estimators by shrinking towards a pooled mean, demonstrating their minimaxity and superior performance through simulations.

Contribution

It introduces empirical and hierarchical Bayes estimators that are minimax and outperform standard preliminary test estimators in multivariate mean problems.

Findings

Bayesian estimators are minimax.

Proposed estimators outperform traditional methods in simulations.

Shrinkage towards pooled mean improves estimation accuracy.

Abstract

In this paper, we consider the estimation of a mean vector of a multivariate normal population where the mean vector is suspected to be nearly equal to mean vectors of $k-1$ other populations. As an alternative to the preliminary test estimator based on the test statistic for testing hypothesis of equal means, we derive empirical and hierarchical Bayes estimators which shrink the sample mean vector toward a pooled mean estimator given under the hypothesis. The minimaxity of those Bayesian estimators are shown, and their performances are investigated by simulation.