doi:10.16186/j.cnki.1673-9787.2020.4.18

Received:2019/11/19

Revised:2020/01/16

Published:2020/07/15

Variable selection in regularized expectile regression with heteroscedasticity

LI Shunyong1, WEI Xiali1, ZHANG Xiaoqin2

1.School of Mathmatical Sciences，Shanxi University，Taiyuan  030006，Shanxi，China；2.School of Statistics，Shanxi University of Finance and Economics,Taiyuan  030006，Shanxi， China

Abstract:Ordinary least square regression is invalid when the heteroscedasticity exists. To solve the problem of regression model construction and variable selection when the heteroscedasticity existed， based on expectile regression which relied on asymmetric L₂ norm the regularized expectile regression with minimax concave penalty（MCP）was proposed to achieve the variable selection and heteroscedasticity detection simultaneously，and more complete relationship between the response variable and predictors was captured. Existing achievements mostly based on the assumption that the error followed normal distribution or it was independent and identically distributed. The proposed method weakened this assumption to the assumption that the random errors were independent but different distributions（non-iid）and had finite moments. Under some conditions，the Oracle property of the proposed estimator was obtained.Numerical simulation showed that the proposed method had good performance in variable selection and could detect heteroscedasticity efficiently according to the change of covariates set under different expectile values.

Key words:Expectile regression;minmax concave;heteroscedasticity;non-concave penalty;variable selection;Oracle property

异方差下正则化Expectile回归的变量选择_李顺勇.pdf