平衡损失下回归系数的最优估计  

The optimal estimations of regression coefficient under balanced loss function

作　　者：胡桂开[1] 饶志勇[1] 虞先玉[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《湖北大学学报（自然科学版）》2010年第3期261-264,共4页Journal of Hubei University：Natural Science

基　　金：东华理工大学校长基金(DHXK0912)资助

摘　　要：主要研究一般Gauss-Markov模型中回归系数的最优估计问题.在平衡损失下,考虑回归系数的线性估计在线性无偏估计类中的最小风险性,得到回归系数的最优线性无偏估计,并证明最优线性无偏估计在几乎处处意义下的唯一性.特别地,考虑了一类特殊的估计:b-线性估计;获得了回归系数的最优b-线性无偏估计,结果表明最优线性无偏估计也是回归系数的最优b-线性无偏估计.In this paper,the optimal estimations of regression coefficient in the Gauss-Markov model were investigated.Under balanced loss function,the minimum risk properties of linear estimators of regression coefficient in the class of linear unbiased estimations were considered.The best linear unbiased estimators,which were unique with probability one,were obtained.Specially,a class of particular estimation： b-linear estimation was considered.The optimal b-linear unbiased estimators were obtained.It showed that the optimal linear unbiased estimators were also the optimal b-linear unbiased estimators of regression coefficient.

关 键 词：一般GAUSS-MARKOV模型 平衡损失 最优估计 b-线性估计 

分 类 号：O212.1[理学—概率论与数理统计]