  We consider estimation of a normal mean matrix under the Frobenius loss.
Motivated by the Efron--Morris estimator, a generalization of Stein's prior has
been recently developed, which is superharmonic and shrinks the singular values
towards zero. The generalized Bayes estimator with respect to this prior is
minimax and dominates the maximum likelihood estimator. However, here we show
that it is inadmissible by using Brown's condition. Then, we develop two types
of priors that provide improved generalized Bayes estimators and examine their
performance numerically. The proposed priors attain risk reduction by adding
scalar shrinkage or column-wise shrinkage to singular value shrinkage. Parallel
results for Bayesian predictive densities are also given.
