线性回归模型系数Stein估计的改进研究

Research of improvement of Stein estimators of coefficients in linear regression models

针对线性回归模型病态的根本原因,提出了一类新的估计———c-k型估计,将岭估计与Stein估计统一到一个估计类;研究了这一估计类,证明利用岭回归技术可以改进著名的Stein估计(在均方误差意义下);同时研究了相应参数的最优值,分别给出了它的一个上界及下界,为病态线性回归模型系数的有偏估计提供了改进的技术途径.

In the light of the essence of the ill condition in the linear regression model, this paper first proposes the c-k class of estimators of the coefficients, which combines the ridge regression estimators and the Stein shrinkage estimators into a bigger class of estimators. The c-k class of estimators is studies, and it is proved that under the mean square error criterion the Stein estimators can be improved via the ridge regression technique. Then the optimal value of the parameters is examined and each of its upper bounds and lower bounds is given respectively, which provides a technical way to the improvement of the biased estimators of the coefficients in the linear regression models.