线性回归诊断中的高杠杆点度量

High-leverage Measures in Linear Regression Diagnostics

本文基于线性回归模型提出了一种新的影响度量矩阵,通过对其性质的研究及从数据加权扰动角度分析指出了其对角元比传统度量意义更加鲜明,更易识别出高杠杆点。在此基础上提出岭估计下的影响度量矩阵,进一步提出并研究了岭估计的高杠杆点度量,得到岭估计与最小二乘估计在数据加权扰动时的高杠杆影响变化程度相同的结论,并指出其比前人文献中的度量形式更加简洁。

In this paper, a new measure of influence matrix is presented for ordinary linear models. Through investigating the properties of the measure and analyzing from the perspective of data＇s weight perturbation, it is shown that the diagonal element of the influence matrix is more meaningful and more simple to detect high-leverage points than the traditional measure. ~rther, based on the results for ordinary linear models, the measure of influence matrix for ridge regression is derived, and high-leverage measure for ridge estimation is also obtained and investigated. It is concluded that the relative variation of high-leverage influence for both of least squares estimation and ridge estimation are the same under the perturbation of weights for data. The high-leverage measure for ridge regression derived in this paper is simpler than that in the literature.