平衡损失下正态线性模型中回归系数的非线性估计及其性质  

The nonlinear estimation and its properties of regression coefficient in normal linear model under balanced loss function

作　　者：彭萍[1] 胡桂开[1] 

机构地区：[1]东华理工大学理学院,抚州344000

出　　处：《黑龙江大学自然科学学报》2012年第6期776-780,共5页Journal of Natural Science of Heilongjiang University

基　　金：江西省教育厅科学技术研究项目(GJJ12388)

摘　　要：在平衡损失函数下,研究正态线性模型中回归系数的非线性估计。首先获得了齐次线性估计类中回归系数的最小风险估计,结果表明最小风险估计与未知参数有关,在应用上为非线性的。其次在最小风险估计的基础上给出一个改进非线性估计,并基于平衡损失风险准则得到非线性估计优于普通最小二乘估计的充分条件。最后证明在适当的假设下,该非线性估计在Pitman准则下一致优于普通最小二乘估计。Under balanced loss function, the nonlinear estimation of regression coefficient in a normal linear regres- sion model is investigated. Firstly, the minimum risk estimation of regression coefficient is obtained. The result shows that the minimum risk estimation is connected with unknown parameters, and it is nonlinear in practice. Sec- ondly, on the basis of the minimum risk estimation, an improved nonlinear estimation is given. Sufficient conditions for the nonlinear estimation to be better than the ordinary least squares estimation are obtained. Finally, under proper hypothesis, it is shown that the nonlinear estimation is uniformly better than the ordinary least squares esti- mation under Pitman criterion.

关 键 词：回归系数 非线性估计 平衡损失 PITMAN准则 

分 类 号：O212.1[理学—概率论与数理统计]