Stein's idea and minimax admissible estimation of a multivariate normal mean

We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of minimax admissible estimator which are generalized Bayes with respect to a prior distribution which is a mixture of a point prior at the origin and a continuous hierarchical type prior. We also study conditions under which these generalized Bayes minimax estimators improve on the James-Stein estimator and on the positive-part James-Stein estimator. (C) 2003 Elsevier Inc. All rights reserved.