Estimation of the noncentrality matrix of a noncentral Wishart distribution with unit scale matrix. A matrix generalitzation of Lenng's domination result

Abstract

The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung’s but generalized to a matrix loss function. Parallelly Leung’s scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of L¨owner partial ordering of symmetric matrices is used.