The superiority of bayes estimators in a multivariate linear model with respect to normal-inverse Wishart prior

Abstract

In this paper, the multivariate linear model Y = XB+e, e ∼ Nm×k(0, Im⊗Σ) is considered from the Bayes perspective. Under the normal-inverse Wishart prior for (B, Σ), the Bayes estimators are derived. The superiority of the Bayes estimators of B and Σ over the least squares estimators under the criteria of Bayes mean squared error (BMSE) and Bayes mean squared error matrix (BMSEM) is shown. In addition, the Pitman Closeness (PC) criterion is also included to investigate the superiority of the Bayes estimator of B.