Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models

Yunquan Song, Zitong Li and Minglu Fang
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Yunquan Song: College of Science, China University of Petroleum, Qingdao 266580, China
Zitong Li: College of Science, China University of Petroleum, Qingdao 266580, China
Minglu Fang: College of Science, China University of Petroleum, Qingdao 266580, China

Mathematics, 2022, vol. 10, issue 12, 1-17

Abstract: The single-index model is an intuitive extension of the linear regression model. It has been increasingly popular due to its flexibility in modeling. In this work, we focus on the estimators of the parameters and the unknown link function for the single-index model in a high-dimensional situation. The SCAD and Laplace error penalty (LEP)-based penalized composite quantile regression estimators, which could realize variable selection and estimation simultaneously, are proposed; a practical iterative algorithm is introduced to obtain the efficient and robust estimators. The choices of the tuning parameters, the bandwidth, and the initial values are also discussed. Furthermore, under some mild conditions, we show the large sample properties and oracle property of the SCAD and Laplace penalized composite quantile regression estimators. Finally, we evaluated the performances of the proposed estimators by two numerical simulations and a real data application.

Keywords: single-index models; composite quantile regression; SCAD; Laplace error penalty (LEP) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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