Independence distribution preserving covariance structures for the multivariate linear model

Consider the multivariate linear model for the random matrix Y(n x p)simila r to MN(XB,Vx Sigma), where B is the parameter matrix, X is a model matrix, not necessarily of full rank, and V x Sigma is an np x np positive-definit e dispersion matrix. This paper presents sufficient conditions on the posit ive-definite matrix V suck that the statistics for testing H-0: CB = 0 vs H -a: CB not equal 0 have the same distribution as under the i.i.d. covarianc e structure I x Sigma. (C) 1999 Academic Press. AMS 1985 subject classifica tions: 62H15, 62K15.