Gauss—Markoff模型中回归系数的线性Bayes估计

BAYES LINEAR ESTIMATES OF REGRESSION COEFFICIENT IN A GENERAL GAUSS -MARKOFF MODEL

考虑一般的Gauss-Markoff模型Y=Xβ+ε,E(ε)=0,cov(ε)=σ~2V,其中X,V≥0分别是n×p,n×n已知矩阵,β∈R^P,σ~2>0是未知参数,设Sβ是线性可估的,则在平方损失和矩阵损失下,分别给出了所有线性Bayes估计,并指出一些线性Bayes估计是线性可容许估计,对Y是正态情形给出了一类在整个估计类中是β的可容许的线性Bayes估计。

In consideration of the generalized Gauss-Markoff Model Y = xβ+ε, E(ε) = 0> COV(ε) = σ2V, where X and V≥0 are the known matrices, βεRP and σ2>0 are parameters. Let Sβ be linearly estimable. With respect to the priors of βπ1, Eπ1(β) = 0, Covπ1(β) = σ2W and π2, Eπ2(β) = 0, Covπ2(β) = σ-W under the quadratic loss function and matrix loss function, all Bayes linear estimators are obtained. Some of them are admissible among linear estimators. If Y is a normal vector, a class of admissible estimators of mean β among all the estimators under quadratic loss function is obtained.