Electronic Journal of Statistics

Significance testing in quantile regression

Stanislav Volgushev, Melanie Birke, Holger Dette, and Natalie Neumeyer

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We consider the problem of testing significance of predictors in multivariate nonparametric quantile regression. A stochastic process is proposed, which is based on a comparison of the responses with a nonparametric quantile regression estimate under the null hypothesis. It is demonstrated that under the null hypothesis this process converges weakly to a centered Gaussian process and the asymptotic properties of the test under fixed and local alternatives are also discussed. In particular we show, that - in contrast to the nonparametric approach based on estimation of $L^{2}$-distances - the new test is able to detect local alternatives which converge to the null hypothesis with any rate $a_{n}\to 0$ such that $a_{n}\sqrt{n}\to\infty$ (here $n$ denotes the sample size). We also present a small simulation study illustrating the finite sample properties of a bootstrap version of the corresponding Kolmogorov-Smirnov test.

Article information

Electron. J. Statist., Volume 7 (2013), 105-145.

First available in Project Euclid: 24 January 2013

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G08: Nonparametric regression
Secondary: 62G30: Order statistics; empirical distribution functions

Nonparametric quantile regression significance testing empirical processes monotone rearrangement


Volgushev, Stanislav; Birke, Melanie; Dette, Holger; Neumeyer, Natalie. Significance testing in quantile regression. Electron. J. Statist. 7 (2013), 105--145. doi:10.1214/12-EJS765. https://projecteuclid.org/euclid.ejs/1359041587

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