A new class of Bayes minimax estimators of the normal mean matrix for the case of common unknown variances

This note considers the problem of estimating the mean matrix Θ of a matrix-variate normal distribution with the covariance matrix σ2Ip⊗Im when the loss function is tr((δ−Θ)(δ−Θ)′)/σ2, where σ2 is unknown. We find a large class of (proper and generalized) Bayes minimax estimators for the mean matrix. This class includes classes of estimators obtained by Tsukuma Proper Bayes minimax estimators of the normal mean matrix with common unknown variances. J Statist Plan Inference. 2010;140:2596–2606.