矩阵损失下贝叶斯线性无偏估计及其稳健性  

Bayesian linear unbiased estimator and its robustness under the matrix loss function

作　　者：邱红兵[1] 罗季[2] 

机构地区：[1]广东工业大学应用数学学院,广州510520 [2]浙江财经学院数学与统计学院,杭州310018

出　　处：《华东师范大学学报（自然科学版）》2013年第1期24-29,53,共7页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11171058;11271317);浙江省自然科学基金(Y6110615;LY12A01017);国家社科基金(11CTJ008)

摘　　要：证明了,在一般线性模型中,未知参数在二次损失下的贝叶斯线性无偏估计也是矩阵损失下的贝叶斯线性无偏估计.讨论了贝叶斯线性无偏估计关于误差分布的稳健性,给出了未知参数的贝叶斯线性无偏估计是最优估计的充分必要条件.It was proved that the Bayesian linear unbiased estimator of the unknown parameters in a general linear model under the quadratic loss function is also the Bayesian linear unbiased estimator under the matrix loss function. The robustness of the Bayesian linear unbiased estimator of the unknown parameter in terms of error distributions was also discussed; moreover, the necessary and sufficient conditions are obtained, under which the Bayesian linear unbiased estimator of the unknown parameters hold its optimality.

关 键 词：线性模型 贝叶斯线性无偏估计 稳健性 

分 类 号：O212.8[理学—概率论与数理统计]