基于奇异值分解的岭型回归(英文)  

Ridge Type Regression Based on Singular Value Decomposition

作　　者：归庆明[1] 郭建峰[1] 李国重[1] 

机构地区：[1]信息工程大学理学院数理系,河南郑州450001

出　　处：《应用数学》2004年第S2期46-52,共7页Mathematica Applicata

基　　金：Supported by Natural Science Foundation of China(4047400;40074006) and NationalScience Fund of China for Distinguished Young Scholars of China(40125013).

摘　　要：本文基于设计阵的奇异值分解(SVD),从LS估计出发,应用岭回归估计方法,构造了回归系数的一个新的有偏估计,称为基于SVD的岭型回归估计,简称RRSVD估计,讨论了其性质和偏参数的选取问题,得到了许多重要结论.计算结果表明,在设计阵呈病态时,RRS善岭回归估计.In this paper,we propose a new biased estimator of regression coefficients by combining the singular value decomposition (SVD) of the design matrix and the ordinary ridge regression (ORR) estimation method,which is called ridge type regression estimator based on SVD (RRSVD estimator).The RRSVD estimator is compared with the OLS estimator in terms of the mse and under the Pitman's measure of closeness,respectively.A numerical example is utilized to illustrate that the RRSVD estimator can overcome multicollinearity effectively,and that the numerical stability of the RRSVD estimator is preferable to the ORR estimator.

关 键 词：复共线性 奇异值分解 岭回归 

分 类 号：O211.6[理学—概率论与数理统计]