A penalized approach to covariate selection through quantile regression coefficient models. (August 2020)

• Record Type: Journal Article
• Authors: Sottile, Gianluca; Frumento, Paolo; Chiodi, Marcello; Bottai, Matteo
• Is Part Of: Statistical modelling. Volume 20:Number 4(2020)
• Page Start: 369
• Page End: 385
• Publication Date: 2020-08
• Subjects: inspiratory capacity -- Lasso penalty -- Penalized integrated loss minimization (PILM) -- penalized quantile regression coefficients modelling (QRCMp) -- tuning parameter selection; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X19825523
• Languages: English
• ISSNs: 1471-082X

Abstract

The coefficients of a quantile regression model are one-to-one functions of the order of the quantile. In standard quantile regression (QR), different quantiles are estimated one at a time. Another possibility is to model the coefficient functions parametrically, an approach that is referred to as quantile regression coefficients modeling (QRCM). Compared with standard QR, the QRCM approach facilitates estimation, inference and interpretation of the results, and generates more efficient estimators. We designed a penalized method that can address the selection of covariates in this particular modelling framework. Unlike standard penalized quantile regression estimators, in which model selection is quantile-specific, our approach permits using information on all quantiles simultaneously. We describe the estimator, provide simulation results and analyse the data that motivated the present article. The proposed approach is implemented in theqrcmNP package in R.