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

摘要

Consider a mixed effects linear model Y = X#xDF;+E, where Y #x20AC; Rnlis a vector of observations, B #x20AC; Rn1is mixed effects satisfying #xDF; = Ad + d with d N(0, o2d), d #x20AC; Rk,1is fixed effects and d #x20AC; Rp,lis random effects, which is uncorrelated withEN(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 Sd+ Q#xDF; to be admissible in the class of linear estimators under the matrix risk are given