Best Linear Unbiased Estimation for the Aitken Model

Abstract

Recall from Chap. 7 that the least squares estimators of estimable functions are best linear unbiased estimators (BLUEs) of those functions under the Gauss–Markov model. But it turns out that this is not necessarily so under linear models having a more general variance–covariance structure, such as the Aitken model. In this chapter, we consider estimators that are best linear unbiased under the Aitken model . The first section considers the special case of an Aitken model in which the variance–covariance matrix is positive definite; BLUE in this case is also called generalized least squares estimation. The second section considers the general case. The third section characterizes those Aitken models for which the least squares estimators of estimable functions are BLUEs of those functions. A final section briefly considers an attempt to extend BLUE to the general mixed linear model.