The linear minimax estimator of stochastic regression coefficients and parameters under quadratic loss function

Consider stochastic effects linear model Y=Xβ+ε with E(β)=Aα,Cov(β)=σ2V1, E(ε)=0,Cov(ε)=σ2V2, and E(βε′)=0, where V1 and V2 are known positive definite matrices, α∈Rk and σ2>0 are unknown parameters. In this paper, we consider a particular quadratic loss function . On the basis of this we obtain the unique linear minimax estimator of the linear estimable function Sα+Qβ.