Adaptive Bi-Level Variable Selection for Quantile Regression Models with a Diverging Number of Covariates

Xianwen Ding and Zhihuang Yang ()
Additional contact information
Xianwen Ding: Department of Statistics, Jiangsu University of Technology, Changzhou 213001, China
Zhihuang Yang: Key Laboratory of Statistical Modeling and Data Analysis of Yunnan Province, Yunnan University, Kunming 650500, China

Mathematics, 2024, vol. 12, issue 20, 1-23

Abstract: The paper develops an innovatively adaptive bi-level variable selection methodology for quantile regression models with a diverging number of covariates. Traditional variable selection techniques in quantile regression, such as the lasso and group lasso techniques, offer solutions predominantly for either individual variable selection or group-level selection, but not for both simultaneously. To address this limitation, we introduce an adaptive group bridge approach for quantile regression, to simultaneously select variables at both the group and within-group variable levels. The proposed method offers several notable advantages. Firstly, it adeptly handles the heterogeneous and/or skewed data inherent to quantile regression. Secondly, it is capable of handling quantile regression models where the number of parameters grows with the sample size. Thirdly, via employing an ingeniously designed penalty function, our method surpasses traditional group bridge estimation techniques in identifying important within-group variables with high precision. Fourthly, it exhibits the oracle group selection property, implying that the relevant variables at both the group and within-group levels can be identified with a probability converging to one. Several numerical studies corroborated our theoretical results.

Keywords: quantile regression; bi-level variable selection; adaptive bridge estimator; diverging parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/20/3284/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/20/3284/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:20:p:3284-:d:1502531

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().