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2013 Significance testing in quantile regression
Stanislav Volgushev, Melanie Birke, Holger Dette, Natalie Neumeyer
Electron. J. Statist. 7: 105-145 (2013). DOI: 10.1214/12-EJS765


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.


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Stanislav Volgushev. Melanie Birke. Holger Dette. Natalie Neumeyer. "Significance testing in quantile regression." Electron. J. Statist. 7 105 - 145, 2013.


Published: 2013
First available in Project Euclid: 24 January 2013

zbMATH: 1337.62084
MathSciNet: MR3020416
Digital Object Identifier: 10.1214/12-EJS765

Primary: 62G08, 62G10
Secondary: 62G30

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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