Bayes minimax estimators of a multivariate normal mean

Abstract

Let X have a p-dimensional normal distribution with mean vector θ and identity covariance matrix I. In a compound decision problem consisting of squared error estimation of θ based on X, a prior distribution Λ is placed on a normal class of priors to produce a family of Bayes estimators t̂. Let g( w) be the density of the prior distribution Λ. If wg′(w) g(w) does not change sign and is bounded, t̂ is minimax. This condition is different from the condition obtained by Faith (1978), where wg′(w) g(w) is nonincreasing. Based on this condition, we obtain several new families of minimax Bayes estimators.