Dong Wang

Victoria University of Wellington

Properties of a random matrix from a multivariate normal distribution

In this communication, we consider a p by n random matrix X = (x_1, ..., x_n) from a pn dimensional multivariate normal distribution, where x_i and x_j are correlated. The covariance matrix of x_i and x_j is given by the p by p matrix V_{ij} and each x_i is from a p dimensional multivariate normal distribution with a mean vector and a covariance matrix which is given by the Kronecker product. The statistical objective is to consider the maximum likelihood estimate of the mean matrix and various components of the covariance matrix and their statistical applications. Some properties of these estimators are also investigated in this paper.