Invariance of the BLUE under the linear fixed and mixed effects models

Abstract

We consider the estimation of the parametric function X₁β₁ under the partitioned linear fixed effects model y=X₁β₁+X₂β₂+ε and the linear mixed effects model y=X₁β₁+X₂γ₂+ε,  where γ₂ is considered to be a random vector. Particularly, we consider when the best linear unbiased estimator, BLUE, of X₁β₁ under the linear fixed effects model equals the corresponding BLUE under the linear mixed effects model.