Linear sufficiency and completeness in the context of estimating the parametric function in the general Gauss-Markov model

In this paper we consider linear sufficiency and linear completeness in the context of estimating the estimable parametric function K′β under the general Gauss-Markov model {y,Xβ,σ2V}. We give new characterizations for linear sufficiency, and define and characterize linear completeness in a case of estimation of K′β. Also, we consider a predictive approach for obtaining the best linear unbiased estimator of K′β, and subsequently, we give the linear analogues of the Rao-Blackwell and Lehmann-Scheffé Theorems in the context of estimating K′β.