Estimation under matrix quadratic loss and matrix superharmonicity

Summary We investigate estimation of a normal mean matrix under the quadratic loss. Improved loss implies improved any linear combination columns First, an unbiased estimate risk is derived and Efron–Morris estimator shown to be minimax. Next, notion superharmonicity for matrix-variate functions introduced have properties analogous those usual superharmonic functions, which may independent interest. Then, it that generalized Bayes with respect prior also provide class priors includes previously proposed generalization Stein’s prior. Numerical results demonstrate work well low-rank matrices.