Bayes minimax estimators of a multivariate normal mean

Let X have a p-dimensional normal distribution with mean vector [theta] and identity covariance matrix I. In a compound decision problem consisting of squared error estimation of [theta] based on X, a prior distribution [Lambda] is placed on a normal class of priors to produce a family of Bayes estimators t. Let g(w) be the density of the prior distribution [Lambda]. If wg'(w)/g(w) does not change sign and is bounded, t 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.