A note on minque for normal models

Abstract

Consider a normal linear model where e has covariance matrix with c = (c1 … cp) ′ unknown. Restricting estimators to the class of functions for all β we prove, that Minque is locally minimum variance unbiased estimator. This result is extended to the class of all unbiased estimators if the range of X is assumed to be an invariant subspace with respect to all linear mappings given by V 1 … Vp . Furthermore necessary and sufficient conditions for the existence of uniformly best unbiased estimators (BUE) or only uniformly best invariant unbiased estimators (BIUE) are developed. They are small extensions of earlier results published by C.R. Rao [7] and J. Seely [8]. A sufficient condition for a BUE t exist given in 8, is shown to be not necessary.