On Weighted Sum Decompositions of Weighted Least-squares Estimators

摘要

For the partitioned linear model M={y, Xβ, σ2 ∑}={y, X1β2 + X2β2, σ2 ∑}, in this paper, a necessary and sufficient condition of the following weighted sum decomposition WLSEM (Xβ) = αWLSEM1(X1β1) + δWLSEM2 (X2β2),is derived, where α+δ=1, α>0,δ> 0.