线性回归模型系数的一个新的有偏估计

New Class of Biased Estimators of Coefficients in Linear Regression Models

针对引起线性回归模型病态的根本原因,提出回归系数的S-R估计,讨论其均方误差的最优化,对有偏估计的改进进行研究。证明可以选择参数,使它在均方误差的意义下优于系数的Stein估计和LS估计,给出参数的最优值。然后讨论其偏差,证明它的可容许性。

Aiming at the fundamental reason of the ill-condition in the linear regression models, presents the S-R estimators of the coefficients, discusses the optimization of its mean squares error and studies the improvement of biased estimators. It is proved that the Stein estimators and the LS estimators can be improved under the mean squares error criterion by choosing appropriate parameters respectively, and the optimal values of the parameters are also obtained. Its deviation from the regression coefficients is also studied. At last its admissibility is proved.