Asymptotic optimality of estimators in multiyariate linear models

Abstract

This paper deals with asymptotic properties of the Least-Square Estimator and of two-stage estimators in multiariate linear models where the case of singular experimental matrices is included. Fristly we prove the asymptotic optimality of the best linear unbiased estimator (BLUE) when the convariance matrix is assumed to be known in a partial class of linear asymptotically unbiased and consistent sequences of estimators. Comparison of two sequences is made by the help of limits of covariance matrices. Secondly conditions are given under which sequence of Blue's. Furthermore there are a lot of cases in which the ineffienent ordinary Least-Square Estimator (OLSE) becomes asymptotically an efficient estimator when the sample size increases. General conditions are obtained under which this fact holds. Certain examples are discussed for illustration.