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June 2016 Inference for single-index quantile regression models with profile optimization
Shujie Ma, Xuming He
Ann. Statist. 44(3): 1234-1268 (June 2016). DOI: 10.1214/15-AOS1404

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.

Citation

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Shujie Ma. Xuming He. "Inference for single-index quantile regression models with profile optimization." Ann. Statist. 44 (3) 1234 - 1268, June 2016. https://doi.org/10.1214/15-AOS1404

Information

Received: 1 April 2015; Revised: 1 October 2015; Published: June 2016
First available in Project Euclid: 11 April 2016

zbMATH: 1338.62119
MathSciNet: MR3485959
Digital Object Identifier: 10.1214/15-AOS1404

Subjects:
Primary: 62G08
Secondary: 62G20

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 3 • June 2016
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