Independence Distribution Preserving Covariance Structures for the Multivariate Linear Model

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