Bayesian Statistical Inference on Elliptical Matrix Distributions

In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parametersμandΣ. Under a noninformative prior distribution, we obtain the posterior distribution, posterior mean, and generalized maximim likelihood estimators ofμandΣ. Under the entropy loss and quadratic loss, the best Bayesian estimators ofΣare derived as well. Some applications are given.