Statistics and Its Interface

Volume 12 (2019)

Number 3

Robust variable selection of varying coefficient partially nonlinear model based on quantile regression

Pages: 397 – 413

DOI: https://dx.doi.org/10.4310/18-SII558

Authors

Jing Yang (Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China; and College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan Province, China)

Fang Lu (Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China; and College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China)

Guoliang Tian (Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong, China)

Xuewen Lu (Department of Mathematics and Statistics, University of Calgary, Alberta, Canada)

Hu Yang (College of Mathematics and Statistics, Chongqing University, Chongqing, China)

Abstract

Quantile regression has been a popular topic for robust inference in semi-parametric models. However, there does not exist related literature for the varying coefficient partially nonlinear model (VCPNLM), which is the focus of this paper. Let alone on the quantile variable selection of VCPNLM. Specifically, via iteratively minimizing an average check loss estimation procedure based on quantile loss function, we propose a profile-type nonlinear quantile regression method for the VCPNLM, and further establish the asymptotic properties of the resulting estimators under some mild regularity conditions. In addition, to achieve sparsity when there exist irrelevant variables, we develop a variable selection procedure for high-dimensional VCPNLM by using the idea of shrinkage, and then demonstrate its oracle property. Two most important parameters including the smoothing parameter and the tuning parameter are also discussed, respectively. Finally, extensive numerical simulations with various errors are conducted to evaluate the finite sample performance of estimation and variable selection, and a real data analysis is further presented to illustrate the application of the proposed methods.

Keywords

varying coefficient partially nonlinear model, quantile regression, variable selection, oracle property, robustness

2010 Mathematics Subject Classification

Primary 62F35. Secondary 62G08, 62G20, 62P12.

Full Text (PDF format)

Jing Yang’s research was partially supported by the National Natural Science Foundation of China (Grant 11801168) and the Natural Science Foundation of Hunan Province (Grant 2018JJ3322).

Fang Lu’s research was partially supported by the National Natural Science Foundation of China (Grants 11801169, 11571055).

Guoliang Tian’s research was partially supported by the National Natural Foundation of China (Grant 11771199).

Xuewen Lu’s research was supported by Discovery Grants (RG/PIN261567-2013) from National Science and Engineering Council of Canada.

Hu Yang’s research was partially supported by the National Natural Science Foundation of China (Grant 11671059).

Received 3 June 2018

Published 4 June 2019