Admissibility of Linear Estimators of Regression Coefficient in a Variance Component Model

Consider the variance component model EY=Xβ,Coy(Y)=Σ~m_(i=1)θ_iV_i,where X:n×p and V_i≥0(i=1,2,…,m)are known,β∈R~p,θ_i≥0 orθ_i0(i=1,2,…,m)are parameters. In this paper,whenμ(X)■μ(V),the sufficient and necessary conditions for a linear estimable estimator of Sβto be admissible in the class of all linear estimators are given under quadratic loss function.