矩阵损失下回归系数的线性估计的可容许性

Admissibility of Linear Estimators of Regression Coefficient under Matrix Loss Function

针对广义的Gauss Markoff模型Y =Xβ +θ ,E(θ) =0 ,Cov(θ) =σ2 V ,其中X和V >0是已知的n×p和n×n矩阵 ;β∈Rp 和σ2 >0是未知参数 ,给出了矩阵损失条件下 ,Sβ的估计LY +a在非齐次线性估计类中可容许的充要条件 .

The generalized Gauss-Markoff model Y=Xβ+θ, E(θ)=0, Cov(θ)=σ 2V is considered, where X and V>0 are known n×p and n×n matrices respectively;β∈R p and σ 2>0 are unknown parameters. The necessary and sufficient condition for LY+a to be an admissible estimator of Sβ in the class of nonhomogenous linear estimators with the matrix loss function is given.