Variable Selection for Generalized Linear Model with Highly Correlated Covariates  

作　　者：Li Li YUE Wei Tao WANG Gao Rong LI 

机构地区：[1]School of Statistics and Data Science,Nanjing Audit University,Nanjing 211815,P.R.China [2]School of Mathematics,Statistics and Mechanics,Beijing University of Technology,Beijing 100124,P.R.China [3]School of Statistics,Beijing Normal University,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第6期1458-1480,共23页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.12001277,12271046 and 12131006)。

摘　　要：The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously,but these existing methods may fail to be consistent for the setting with highly correlated covariates.In this paper,the semi-standard partial covariance(SPAC)method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates,and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions.Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods.

关 键 词：Generalized linear model highly correlated covariates Lasso penalty semi-standard partial covariance variable selection 

分 类 号：O212.1[理学—概率论与数理统计]