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

Consider stochastic effects linear model Y=X[beta]+[epsilon] with E([beta])=A[alpha],Cov([beta])=[sigma]2V1, E([epsilon])=0,Cov([epsilon])=[sigma]2V2, and E([beta][epsilon]')=0, where V1 and V2 are known positive definite matrices, [alpha][set membership, variant]Rk and [sigma]2>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 S[alpha]+Q[beta].