Admissible Estimation for Linear Combination of Fixed and Random Effects in General Mixed Linear Models

Abstract

The general mixed linear model can be denoted by y = X β + Z u + e , where β is a vector of fixed effects, u is a vector of random effects, and e is a vector of random errors. In this article, the problem of admissibility of Q y and Q y + q for estimating linear functions, ϱ = L ′β + M ′ u , of the fixed and random effects is considered, and the necessary and sufficient conditions for Q y (resp. Q y + q ) to be admissible in the set of homogeneous (resp. potentially inhomogeneous) linear estimators with respect to the MSE and MSEM criteria are investigated. We provide a straightforward alternative proof to the method that was utilized by Wu (1988), Baksalary and Markiewicz (1990), and Groß and Markiewicz (1999). In addition, we derive the corresponding results on the admissibility problem under the generalized MSE criterion.