回归系数的广义根方估计及其模拟

Generalized Root Root Estimator of Multiple Linear Regression Coefficients

文献[1,2]中提出了回归系数的根方估计^(k),当回归自变量间存在复共线关系时,^(k)较回归系数的最小二乘估计有所改善,本文将根方估计作一拓广,得出了回归系数的广义根方估计^(K),其中K为对角阵,文中证明了广义根方估计^(K)较^(k)能更有效地改善最小二乘估计,并给出了广义根方估计的显式解,在此基础上,提出了广义根方估计的显式解和一种确定k_i的方法。

The least square estimator of parameters of multiple linear regression is known to be highly variable when the observed matrix is almost singular. A biased estimator-generalized root root estimator,which is based on the ordinary root root estimator proposed by the au-thors(1987) ,is introduced. This biased estimator is another kind of modified least square estimation procedures. It greatly reduces the Mean Square Error of the estimated coefficients. Two methods for performing this procedure are presented. In addtion, the generalized root root estimator is compared with other estimators by means of simulation.