Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance

We construct a broad class of generalized Bayes minimax estimators of the mean of a multivariate normal distribution with covariance equal to σ 2 I p , with σ 2 unknown, and under the invariant loss ‖ δ ( X ) − θ ‖ 2 / σ 2 . Examples that illustrate the theory are given. Most notably it is shown that a hierarchical version of the multivariate Student- t prior yields a Bayes minimax estimate.