Principal single-index varying-coefficient models for dimension reduction in quantile regression

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

2 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)800-818
Journal / PublicationJournal of Statistical Computation and Simulation
Volume90
Issue number5
Online published28 Dec 2019
Publication statusPublished - Mar 2020

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.

Research Area(s)

  • Asymptotics, check loss, polynomial splines, single-index models, REDUCED-RANK REGRESSION, VARIABLE SELECTION, EFFICIENT ESTIMATION, LINEAR-MODELS, LIKELIHOOD, SHRINKAGE, DEMAND