Independence Distribution Preserving Covariance Structures for the Multivariate Linear Model

AbstractConsider 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

Multivariate regression analysis with dependent observations: conditions for the invariance of the distribution of the Lawley-Hotelling test for the model utility

In this paper we derive necessary and sufficient conditions on the error covariance structure such that the Lawley-Hotelling statistic for testing model utility is invariant from its distribution under the usual assumption of normal i.i.d. observation vectors. We, therefore, generalize the work of Arnold (1979), Ghosh and Sinha (1980), and Tranquilli and Baldesarri (1988)

Independence-distribution-preserving dependency structures for the modified likelihood ratio test for detecting unequal covariance matrices

The modified likelihood ratio (MLR) test statistic is frequently used to detect unequal covariance matrices. We are concerned with examining this statistic with respect to departures from the usual i.i.d. assumptions on the sample data. In particular we characterize the joint covariance structure of two groups of multivariate normal observations so that the distribution of this MLR test statistic is identical to that under the usual assumption of independent identically distributed observations.Correlated observations Robustness Wishart random matrices Multivariate quadratic forms

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].multivariate quadratic forms Wishart random matrices model robustness common nonnegative definite solutions to a pair of matrix equations