Minimax Shrinkage Estimators and Estimators Dominating the James-Stein Estimator under the Balanced Loss Function

Abstract

This paper is dealing with the shrinkage estimators of a multivariate normal mean and their minimaxity properties under the balanced loss function. We present here two different classes of estimators: the first which generalizes the James-Stein estimator, and show that any estimator of this class dominates the maximum likelihood estimator (MLE), consequently it is minimax, and the second dominates the James-Stein estimator and we conclude that any estimator of this class is also minimax.