Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures
Let X be distributed as matrix normal with mean M and covariance matrix W circle times V, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochran's theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor. (C) 2003 Elsevier Inc. All rights reserved
Vaish, A., & Chaganty, N. R. (2004). Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures. Linear Algebra and Its Applications, 388, 379-388.