Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model

Abstract

In this article we consider the partitioned fixed linear model F : y = X₁β₁ + X₂β₂ + ε" and the corresponding mixed model M : y =X₁β₁+X₂u+ ε, where ε is a random error vector and u is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of β₁ in the fixed model F remains BLUE in the mixed model M . In this paper we extend the results concerning further equalities arising from models F and M.