Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution

Abstract

a b s t r a c tThis paper deals with the problem of estimating the mean matrix in an elliptically contoured distribution with unknown scale matrix. The Laplace and inverse Laplace transforms of the density allow us not only to evaluate the risk function with respect to a quadratic loss but also to simplify expressions of Bayes estimators. Consequently, it is shown that generalized Bayes estimators against shrinkage priors dominate the unbiased estimator.

A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution

“…For the problem of estimating the mean matrix of an elliptically contoured distribution, Ref. [19] derived generalized Bayes minimax estimators for the mean matrix; ref. [20] also obtained a class of minimax estimators for the mean matrix, which was used to find a class of proper Bayes minimax estimators of Θ.…”

Bayesian analysis in multivariate regression models with conjugate priors

“…Interested readers may refer to papers by Zellner, [1] Singh et al, [2] Jammalamadaka et al, [3] Chib et al, [4] Osiewalski and Steel, [5] and more recently Fang and Li, [6] Branco et al, [7] Ng, [8][9][10] Arashi, [11] Vidal and Arellano-Valle, [12] and Tsukuma. [13] However, the case of conjugate Bayesian analysis is neglected in matrix elliptical models. Ng [9] showed that when random responses in a multivariate regression model (MRM) have multivariate scale mixtures of normal distributions, the conjugate Bayesian analysis (for the location parameter) yields identical posterior distribution of the regression parameters to those obtained under independently distributed normal responses.…”