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

Consider the variance component model \ep Y=X\beta,\;\cov(Y)=\tsm_i=1^m\theta_iV_i, where X: n\times p and V_i\geq0\;(i=1,2,\cdots,m) are known, \beta\in R^p, \theta_i\geq0 or \theta_i>0 (i=1,2,\cdots,m) are parameters. In this paper, when \mu(X)\subset\mu(V), the sufficient and necessary conditions for a linear estimable estimator of S\beta to be admissible in the class of all linear estimators are given under quadratic loss function.