SOME RESULTS ON THE ADMISSIBILITY OF A LINEAR ESTIMATOR OF REGRESSION COEFFICIENTS IN THE VARIANCE COMPONENTS MODEL

Consider the variance components model EY=Xβ,VAB（Y）=\sum_i=1^m \theta_i V_i where n×p matrix X and V_i（i=1,2,…,m） are known, andβ∈R^p,θ_i≥0 or θ_i>0（i=1,2,…,m） are parameters. Let Sβ be linear estimable. In this paper, some results for a linear estimator of Sβ to be admissible among linear estimators under the quadratic loss function and matrix loss function are obtained respectively. Under normalitsy assumption, we also consider the admissibility of the linear estimator among all the estimators.