Further remarks on permissible covariance structures for simultaneous retention of BLUEs in linear models

Abstract

We consider the partitioned linear model  M₁₂(V₀) = { y, X₁β₁ + X₂ β₂, V₀ } and the corresponding small model  M₁(V₀) = { y, X₁β₁ , V₀ } . We define the set V_1/12 of nonnegative definite matrices V such that every representation of the best linear unbiased estimator, BLUE, of μ₁ = X₁β₁ under M₁₂(V₀) remains BLUE under M₁₂(V) . Correspondingly, we can characterize the set V₁ of matrices V such that every BLUE of μ₁ = X₁β₁ under M₁(V₀) remains BLUE under M₁(V). In this paper we focus on the mutual relations between the sets V₁ and V_1/12 .