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May 2019 Expansion for moments of regression quantiles with applications to nonparametric testing
Enno Mammen, Ingrid Van Keilegom, Kyusang Yu
Bernoulli 25(2): 793-827 (May 2019). DOI: 10.3150/17-BEJ986


We discuss nonparametric tests for parametric specifications of regression quantiles. The test is based on the comparison of parametric and nonparametric fits of these quantiles. The nonparametric fit is a Nadaraya–Watson quantile smoothing estimator.

An asymptotic treatment of the test statistic requires the development of new mathematical arguments. An approach that makes only use of plugging in a Bahadur expansion of the nonparametric estimator is not satisfactory. It requires too strong conditions on the dimension and the choice of the bandwidth.

Our alternative mathematical approach requires the calculation of moments of Nadaraya–Watson quantile regression estimators. This calculation is done by application of higher order Edgeworth expansions.


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Enno Mammen. Ingrid Van Keilegom. Kyusang Yu. "Expansion for moments of regression quantiles with applications to nonparametric testing." Bernoulli 25 (2) 793 - 827, May 2019.


Received: 1 December 2015; Revised: 1 May 2017; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049391
MathSciNet: MR3920357
Digital Object Identifier: 10.3150/17-BEJ986

Keywords: Bahadur expansions , Goodness-of-fit tests , kernel smoothing , Nonparametric regression , Nonparametric testing , quantiles

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability


Vol.25 • No. 2 • May 2019
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