Estimation under a multivariate multiple linear model and some associated reduced models

Abstract

In this study, a multivariate multiple linear model where the model matrix may be defficient in rank and the variance covariance matrix is nonnegative definite, and some associated reduced linear models are considered. In particular, we are interested in the case of coincidence of the best linear unbiased estimators (BLUEs) for the expectation of the observable random matrix under the multivariate multiple linear model and its two reduced linear models. We extend some results in the literature for the multivariate linear model related to BLUE for the expectation of the observable random matrix to those in the multivariate multiple case.