Independence Distribution Preserving Covariance Structures for the Multivariate Linear Model

Consider the multivariate linear model for the random matrixYn×p∼MN(XB, V⊗Σ), whereBis the parameter matrix,Xis a model matrix, not necessarily of full rank, andV⊗Σ is annp×nppositive-definite dispersion matrix. This paper presents sufficient conditions on the positive-definite matrixVsuch that the statistics for testingH0: CB=0vsHa: CB≠0have the same distribution as under the i.i.d. covariance structureI⊗Σ.