Bayesian statistical inference on elliptical matrix distributions

Abstract

In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parameters μ and Σ. Under a noninformative prior distribution, we obtain the posterior distribution, posterior mean, and generalized maximim likelihood estimators of μ and Σ. Under the entropy loss and quadratic loss, the best Bayesian estimators of Σ are derived as well. Some applications are given. © 1999 Academic Press.