Linear sufficiency and completeness in the partitioned linear model

Abstract

In this paper we consider the estimation of X₁β₁ under the partitioned linear model {y,X₁β₁+X₂β₂,σ²V}. In particular, we consider linear sufficiency and linear completeness of X₁β₁. We give new characterizations for linear sufficiency of X₁β₁, and define and characterize linear completeness in a case of estimation of X₁β₁. We also introduce a predictive approach for obtaining the best linear unbiased estimator of X₁β₁, and subsequently, we give linear analogues of the Rao-Blackwell and Lehmann-Scheffé theorems in the context of estimating X₁β₁.