Bayes minimax estimation of the mean matrix of matrix-variate normal distribution under balanced loss function

This note considers the problem of simultaneous estimation of matrix-variate normal mean matrix using a balanced loss function when common variance σ2 is unknown. We first find a class of minimax estimators for this problem and show that the maximum likelihood estimator is inadmissible. We obtain a large class of (proper and generalized) Bayes minimax estimators for the mean matrix.