Set-induced minimax estimators for a multivariate normal mean

Abstract

Using a pseudo-empirical-Bayes approach, better confidence regions, C ∗(X) , for a multivariate normal mean are proposed in Tseng and Brown (Ann. Statist. 25 (1997) 2228). While C ∗(X) have a uniformly smaller volume than the classical confidence set and retaining the same constant coverage probability, they do not render straightforward point estimator as the usual confidence sets and recentered confidence sets because of their unfamiliar shapes. We propose here to use the centroid of C ∗(X) as its supplementary point estimator. With numerical aid, this estimator is shown to have a smaller mean squared errors than the maximum likelihood estimator, hence a minimax.