On Conditional Applications of Matrix Variate Normal Distribution

In this paper, by conditioning on the matrix variate normal distribution (MVND) the construction of the matrix t-type family is considered, thus providing a new perspective of this family. Some important statistical characteristics are given. The presented t-type family is an extension to the work of Dickey [8]. A Bayes estimator for the column covariance matrix Σ of MVND is derived under Kullback Leibler divergence loss (KLDL). Further an application of the proposed result is given in the Bayesian context of the multivariate linear model. It is illustrated that the Bayes estimators of coefficient matrix under both SEL and KLDL are identical.