EMPIRICAL BAYES ESTIMATION OF THE COVARIANCE-MATRIX OF A NORMAL-DISTRIBUTION WITH UNKNOWN MEAN UNDER AN ENTROPY LOSS

In the estimation of the covariance matrix of the multivariate normal distribution with unknown mean vector, Sinha and Ghosh (1987) proposed & truncated estimator improving on the best invariant one relative to the entropy loss. The purpose of the paper is to derive an empirical Bayes estimator based on conjugate priors and to prove that it is than the Sinha-Ghosh estimator. An empirical Bayes estimator for the generalized variance is also given and it is shown to be identical to the usual Stein type truncated est mator.