  We develop a class of minimax estimators for a normal mean matrix under the
Frobenius loss, which generalizes the James--Stein and Efron--Morris
estimators. It shrinks the Schatten norm towards zero and works well for
low-rank matrices. We also propose a class of superharmonic priors based on the
Schatten norm, which generalizes Stein's prior and the singular value shrinkage
prior. The generalized Bayes estimators and Bayesian predictive densities with
respect to these priors are minimax. We examine the performance of the proposed
estimators and priors in simulation.
