线性模型中回归系数的c-F(K)型估计的研究和应用  

Research and Application of the c-F(K) Class Estimator of Regression Coefficients in Linear Models

作　　者：叶晓枫[1] 王珑云 

机构地区：[1]华北水利水电大学,河南郑州450045

出　　处：《华北水利水电学院学报》2013年第5期120-123,共4页North China Institute of Water Conservancy and Hydroelectric Power

基　　金：河南省自然科学基金(112300410040)

摘　　要：针对引起线性回归模型最小二乘估计性能变坏的根本原因,在线性回归模型中提出了一种新的有偏估计β^(F(K))=(cX'V-1X+TF(K)T')-1X'V-1Y,它将众多经典的有偏估计结合在一起,对有偏估计进行了改进.首先利用Stine式压缩技术说明在均方误差意义下β^(F(K))具有优于广义岭估计的优良性质,然后将β^(F(K))应用到多元线性回归模型的可容许性上.Aiming at the fundamental reason for the bad performance of the least squares estimation of the coefficients in the linear regression models, a new class of biased estimation of regression coefficient β（F（K））=（cX＇V-1X＋TF（K）T＇）-1X＇V-1Y is given, which combines various classical biased estimators into a bigger class of estimators. Then the improvement of the biased estimators is studied. Firstly, the idea of Stein regression is applied in this class of biased estimation to obtain a new estimate, which is proved superior to the generalized ridge estimate. And then, β（F（K）） is applied in the admissibility of a multiple linear regression model.

关 键 词：复共线性 最小二乘估计 c-F(K)型估计 可容许性 

分 类 号：O213[理学—概率论与数理统计]