Comparing the BLUEs Under Two Linear Models

Abstract

In this article, we consider two linear models, ℳ₁ = {y, X β, V ₁} and ℳ₂ = {y, X β, V ₂}, which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of X β under these models. The corresponding problems between the models {y, X β, I _n } and {y, X β, V}, i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of X β under ℳ₁ and ℳ₂. This article is an expository one presenting also new results.

Keywords:

• BLUE
• Gauss–Markov model
• Linear sufficiency
• Löwner ordering
• OLSE
• Orthogonal projector

Mathematics Subject Classification:

• 15A42
• 62J05
• 62H12
• 62H20

Acknowledgments

Thanks go to the Associate Editor and the referees for constructive remarks yielding a clarified structure of the article.