Subjective Bayesian analysis of elliptical models

Abstract

The problem of estimation has been widely investigated with all different kinds of assumptions. This study focusses on the subjective Bayesian estimation of a location vector and characteristic matrix for the univariate and multivariate elliptical model as oppose to objective Bayesian estimation that has been thoroughly discussed (see Fang and Li (1999) amongst others). The prior distributions that will be assumed is the conjugate normal-inverse Wishart prior and also the normal-Wishart prior which has not yet been considered in literature. The posterior distributions, joint and marginal, as well as the Bayes estimators will be derived. The newly developed results are applied to the multivariate normal and multivariate t-distribution. For subjective Bayesian analysis the vector-spherical matrix elliptical model is also studied.