Nonnegative Definiteness of the Estimated Dispersion Matrix in a Multivariate Linear Model.

摘要

Estimation is considered in model where both the mean vector and the dispersion matrix have linear decompositions. It is shown that after an invariance reduction with respect to mean translation, MINQUE provides a nonnegative definite estimate of the dispersion matrix, when the decomposing matrices span a quadratic subspace of symmetric matrices. With normality, MINQUE is seen to equal the restricted maximum likelihood estimate and to be of uniformly minimum variance. (Author)