线性回归模型系数有偏估计研究

Research on The Biased Estimators of Coefficients in Linear Regression Models

针对引起线性回归模型LS估计性能变坏的根本原因,提出了回归系数的广义c-K估计,将众多经典的有偏估计结合在一起,对有偏估计的改进进行了研究,分别证明了最小化均方误差和数量化矩阵K均可对Stein估计进行改进,给出了参数的最优值,为病态线性回归模型系数有偏估计的改进提供了有效途径。

Aiming at the fundamental reason for the bad performance of the LS estimator of the coefficients in the linear regression models,this paper presents the generalized c-K estimators of the coefficients,which combines various classical biased estimators into a bigger class of estimators and studies the improvement of the biased estimators.It is proved that the Stein estimators can be improved by minimizing the mean square error of the generalized c-K estimators or by specializing matrix K respectively,and the optimal values of the parameters are also obtained.The proposed approach provides an effective way to the improvement of the biased estimators of the coefficients in the linear regression models.