SOME RESULTS ON THE ADMISSIBILITY OF A LINEAR ESTIMATOR OF REGRESSION COEFFICIENTS IN THE VARIANCE COMPONENTS MODEL
Ing C · 1990
Consider the variance components model EY=Xβ, VAR(Y)=sum from i=1 to m θ_i V_i where n×p matrix X and V_i≥0(i=1, 2, …, m) are known, and β∈R~p, θ_i≥0 or θ_i0 (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.