Comparison of Estimators of Heteroscedastic Variances in Linear Models

Abstract

Four methods for estimating heteroscedastic variances are discussed in this article: the MINQUE introduced by C.R. Rao [7], the AUE introduced by S.D. Horn, R.A. Horn, and D.B. Duncan [4], the average of the squared residuals, and the sample variance. Properties of these estimators, including translation invariance, existence, bias, consistency, existence of negative estimates, and mean square error (MSE) are compared. In particular, it is shown that the AUE has smaller MSE than either the MINQUE or the sample variance in a wide range of situations.