平衡损失下等式约束模型参数的Minimax估计  

The linear Minimax estimation of the parameter in the equality constraint model under balanced loss function

作　　者：胡桂开[1] 彭萍[1] 罗汉[2] 

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 [2]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《安徽大学学报（自然科学版）》2009年第6期1-5,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(70773038);东华理工大学校长基金资助项目(DHXK0912)

摘　　要：研究等式约束模型中回归系数的线性Minimax估计问题.在改进Zellner提出的平衡损失函数的基础上,分析了齐次线性估计类中等式约束模型中回归系数线性估计损失风险的极大极小性,并得到了回归系数的线性Minimax估计;在适当的假设下,证明了回归系数线性Minimax估计的唯一性.In the paper, the linear Minimax estimation of regression coefficient was investigated in the equality constraint model. Firstly we improved the balanced loss function presented by Zellner, on the basis of that, the Minimax properties of linear estimation of regression coefficient in the equality constraint model in the class of homogeneous linear estimates were considered. The Minimax estimation was obtained. Under suitable hypotheses, we proved that the linear Minimax estimation of regression coefficient is unique.

关 键 词：平衡损失函数 回归系数 MINIMAX估计 

分 类 号：O212.4[理学—概率论与数理统计]