Principal single-index varying-coefficient models for dimension reduction in quantile regression. Issue 5 (23rd March 2020)

• Record Type: Journal Article
• Authors: Zhao, Weihua; Zhang, Fode; Li, Rui; Lian, Heng
• Is Part Of: Journal of statistical computation and simulation. Volume 90:Issue 5(2020)
• Page Start: 800
• Page End: 818
• Publication Date: 2020-03-23
• Subjects: Asymptotics -- check loss -- polynomial splines -- single-index models; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1707831
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: We propose a principal single-index varying-coefficient model focusing on conditional quantiles. In this general and flexible class of models, dimension reduction is achieved in three aspects: first, standard varying-coefficient models can partially avoid curse of dimensionality of large dimensional nonparametric regression; second, a one-dimensional adaptive index is constructed from multiple index variables; finally, the number of independent functions is further reduced by using principal functions. We derive the convergence rate of the estimates and asymptotic normality of the index parameter and the coefficient functions. Penalization can be added straightforwardly to obtain joint variable selection and dimension reduction. Simulations are used to demonstrate the performances and an empirical application is presented.