A Family of Minimax Estimators of the Mean of a Multivariate Normal Distribution

Abstract

A family of estimators, each of which dominates the "usual" one, is given for the problem of simultaneously estimating means of three or more independent normal random variables which have a common unknown variance. Charles Stein [4] established the existence of such estimators (for the case of a known variance) and later, with James [3], exhibited some, both for the case of unknown common variances considered here and for other cases as well. Alam and Thompson [1] have also obtained estimators which dominate the usual one. The class of estimators given in this paper contains those of James and Stein and also those of Alam and Thompson.