• Bernoulli
  • Volume 25, Number 2 (2019), 793-827.

Expansion for moments of regression quantiles with applications to nonparametric testing

Enno Mammen, Ingrid Van Keilegom, and Kyusang Yu

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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.

Article information

Bernoulli, Volume 25, Number 2 (2019), 793-827.

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

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Zentralblatt MATH identifier

Bahadur expansions goodness-of-fit tests kernel smoothing nonparametric regression nonparametric testing quantiles


Mammen, Enno; Van Keilegom, Ingrid; Yu, Kyusang. Expansion for moments of regression quantiles with applications to nonparametric testing. Bernoulli 25 (2019), no. 2, 793--827. doi:10.3150/17-BEJ986.

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