On Sum Decompositions of Weighted Least-Squares Estimators for the Partitioned Linear Model

Abstract

For the partitioned linear model ℳ = {y, X 1 β 1 + X 2 β 2,σ2 Σ}, this article investigates decompositions of weighted least-squares estimator (WLSE) of X 1 β 1 + X 2 β 2 under ℳ as sums of WLSEs under the two small models {y, X 1 β 1,σ2 Σ} and {y, X 2 β 2,σ2 Σ}. Some consequences on the sum decomposition of the unique best unbiased linear estimator (BLUE) of X 1 β 1 + X 2 β 2 under ℳ are also given.