Heteroscedasticity identification and variable selection via multiple quantile regression

AbstractHigh-dimensional data often display heteroscedasticity. If the heteroscedasticity is neglected in the regression model, it will produce inefficient inference for the regression coefficients. Quantile regression is not only robust to outliers, but also accommodates heteroscedasticity. This paper aims to simultaneously carry out variable selection and heteroscedasticity identification for the linear location-scale model under a unified framework. We develop a regularized multiple quantile regression approach simultaneously identifying the heteroscedasticity, seeking common features of quantile coefficients and eliminating irrelevant variables. We also establish the theoretical properties of the proposed method under some regularity conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method, showing that it is able to identify the covariates that affect the variability of the response. We further apply the proposed method to analyse the Wage data.Keywords: Heteroscedasticitypenalty functionquantile regressionvariable selectionMathematics Subject Classifications: 62J0762F12 AcknowledgmentsThe authors would like to thank the Editor and two referees for the constructive suggestions that lead to a significant improvement over the article.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe research was supported by the National Natural Science Foundation of China grant numbers 12271294, 12071248, 12071483, and 72232001, Natural Science Foundation of Liaoning Province grant number 2022-MS-179, Department of Education of Liaoning Province grant number LIKMZ20221565, and United International College (UIC) Start-up Research Fund grant number R72021106, Science Foundation of Ministry of Education of China grant number 20YJC910007.