Open Access
August 2017 Quantile regression for the single-index coefficient model
Weihua Zhao, Heng Lian, Hua Liang
Bernoulli 23(3): 1997-2027 (August 2017). DOI: 10.3150/16-BEJ802


We consider quantile regression incorporating polynomial spline approximation for single-index coefficient models. Compared to mean regression, quantile regression for this class of models is more technically challenging and has not been considered before. We use a check loss minimization approach and employed a projection/orthogonalization technique to deal with the theoretical challenges. Compared to previously used kernel estimation approach, which was developed for mean regression only, spline estimation is more computationally expedient and directly produces a smooth estimated curve. Simulations and a real data set is used to illustrate the finite sample properties of the proposed estimator.


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Weihua Zhao. Heng Lian. Hua Liang. "Quantile regression for the single-index coefficient model." Bernoulli 23 (3) 1997 - 2027, August 2017.


Received: 1 April 2015; Revised: 1 October 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714325
MathSciNet: MR3624884
Digital Object Identifier: 10.3150/16-BEJ802

Keywords: asymptotic normality , B-splines , check loss minimization , Quantile regression , single-index coefficient models

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 3 • August 2017
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