The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator

It is well known that the ordinary least squares estimator of Xβ in the general linear model E _y = Xβ, cov y = σ² V, can be the best linear unbiased estimator even if V is not a multiple of the identity matrix. This article presents, in a historical perspective, the development of the several conditions for the ordinary least squares estimator to be best linear unbiased. Various characterizations of these conditions, using generalized inverses and orthogonal projectors, along with several examples, are also given. In addition, a complete set of references is provided.