The Annals of Statistics

Inference for single-index quantile regression models with profile optimization

Shujie Ma and Xuming He

Full-text: Open access

Abstract

Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a pseudo-profile likelihood approach to estimation and testing for single-index quantile regression models. We establish the asymptotic normality of the index coefficient estimator as well as the optimal convergence rate of the nonparametric function estimation. Moreover, we propose a score test for the index coefficient based on the gradient of the pseudo-profile likelihood, and employ a penalized procedure to perform consistent model selection and model estimation simultaneously. We also use Monte Carlo studies to support our asymptotic results, and use an empirical example to illustrate the proposed method.

Article information

Source
Ann. Statist., Volume 44, Number 3 (2016), 1234-1268.

Dates
Received: April 2015
Revised: October 2015
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1460381692

Digital Object Identifier
doi:10.1214/15-AOS1404

Mathematical Reviews number (MathSciNet)
MR3485959

Zentralblatt MATH identifier
1338.62119

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Keywords
Quantile regression single-index profile principle polynomial spline model selection score test

Citation

Ma, Shujie; He, Xuming. Inference for single-index quantile regression models with profile optimization. Ann. Statist. 44 (2016), no. 3, 1234--1268. doi:10.1214/15-AOS1404. https://projecteuclid.org/euclid.aos/1460381692


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Supplemental materials

  • Supplement to “Inference for single-index quantile regression models with profile optimization”. We present several lemmas that will be used in the proof of the main theorems, and the proof of equation (A.18). Then we present Example 2 for Case 1 and additional simulation results for Case 2 in the simulation studies.