  The estimation of the mean matrix of the multivariate normal distribution is
addressed in the high dimensional setting. Efron-Morris-type linear shrinkage
estimators based on ridge estimators for the precision matrix instead of the
Moore-Penrose generalized inverse are considered, and the weights in the
ridge-type linear shrinkage estimators are estimated in terms of minimizing the
Stein unbiased risk estimators under the quadratic loss. It is shown that the
ridge-type linear shrinkage estimators with the estimated weights are minimax,
and that the estimated weights converge to the optimal weights in the Bayesian
model with high dimension by using the random matrix theory. The performance of
the ridge-type linear shrinkage estimators is numerically compared with the
existing estimators including the Efron-Morris and James-Stein estimators.
