Quadratic Estimation of Variance Components

Abstract

Best quadratic estimators of the variance components in a general linear model are presented for each of several classes of estimators of the form Y'A Y. Of the classes examined, three contain biased estimators and the others contain only unbiased estimators. Attainable lower bounds on mean squared errors of estimators in each class are described. In the classes of unbiased estimators, necessary and sufficient conditions for estimability are established. Normality is assumed throughout.