A simplified version of Cochran's theorem in mixed linear models
Tonghui Wang, Baokun Li, Arjun K. Gupta · Random Operators and Stochastic Equations · 2008
Abstract For a multivariate normally distributed n × p random matrix Y with mean μ and covariance Σ Y = V 1 ⊗Σ 1 + V 2 ⊗Σ 2 , necessary and sufficient conditions, under which Y′WY follows a Wishart distribution, are obtained, where W is a symmetric matrix, V 1 and V 2 are known nonnegative definite matrices, and Σ 1 and Σ 2 are unknown nonnegative definite parameter matrices. Several examples are given to illustrate our main results.