On extension of some identities for the bias and risk functions in elliptically contoured distributions

In this paper, we are interested in an estimation problem concerning the mean parameter of a random matrix whose distribution is elliptically contoured. We derive two general formulas for the bias and risk functions of a class of multidimensional shrinkage-type estimators. As a by product, we generalize some recent identities established in Gaussian sample cases for which the shrinking random part is a single Kronecker-product. Here, the variance–covariance matrix of the shrinking random part is the sum of two Kronecker-products.