Necessary and sufficient conditions that linear estimators of a mixed effects linear model are admissible under matrix loss function

Abstract

Consider a mixed effects linear model Y = Xs+E, where Y € Rnlis a vector of observations, B € Rn1is mixed effects satisfying s = A[d] + [d] with [d] N(0, o2[d]), [d] € Rk,1is fixed effects and [d] € Rp,lis random effects, which is uncorrelated with EN(0, o2V); X, A, [d] and V are known matrices, [d] and V are nonnegative definite. A random effects linear model and a fixed effects linear model are a special case of the above model. Necessary and sufficient conditions for a Linear estimator LY + b of S[d]+ Qs to be admissible in the class of linear estimators under the matrix risk are given