Heteroscedasticity identification and variable selection via multiple quantile regression
High-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...
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Published in | Journal of statistical computation and simulation Vol. 94; no. 2; pp. 297 - 314 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Abingdon
Taylor & Francis
22.01.2024
Taylor & Francis Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | High-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. |
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ISSN: | 0094-9655 1563-5163 |
DOI: | 10.1080/00949655.2023.2243533 |