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 σ2Ipσ2Ip, with σ2σ2 unknown, and under the invariant loss ‖δ(X)−θ‖2/σ2‖δ(X)−θ‖2/σ2. Examples that illustrate the theory are given. Most notably it is shown that a hierarchical version of the multivariate Student-tt prior yields a Bayes minimax estimate.