A Comparison of Two Criteria for Ordinary-Least-Squares Estimators to Be Best Linear Unbiased Estimators

Abstract

Abstract The problem of the equality between ordinary-least-squares estimators and best linear unbiased estimators is discussed in the literature in two versions: in the context of a fixed model (design) matrix and in the context of all model (design) matrices having a fixed common linear part. Unfortunately, one of the criteria derived in the latter case (McElroy 1967) is incorrectly quoted by some authors as a solution to the former version of the problem. This article clarifies the difference between the two versions and shows that there is no practical situation where the corresponding solutions can coincide.