  This paper deals with the problem of estimating predictive densities of a
matrix-variate normal distribution with known covariance matrix. Our main aim
is to establish some Bayesian predictive densities related to matricial
shrinkage estimators of the normal mean matrix. The Kullback-Leibler loss is
used for evaluating decision-theoretical optimality of predictive densities. It
is shown that a proper hierarchical prior yields an admissible and minimax
predictive density. Also, superharmonicity of prior densities is paid attention
to for finding out a minimax predictive density with good numerical
performance.
