Abstract
In this article, we propose a new test for additivity in nonparametric quantile regression with a high-dimensional predictor. Asymptotic normality of the corresponding test statistic (after appropriate standardization) is established under the null hypothesis, local and fixed alternatives. We also propose a bootstrap procedure which can be used to improve the approximation of the nominal level for moderate sample sizes. The methodology is also illustrated by means of a small simulation study, and a data example is analyzed.
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Acknowledgments
The authors thank Martina Stein, who typed parts of this manuscript with considerable technical expertise. We are also grateful to two referees and the associate editor for their constructive comments on an earlier version of this manuscript. This work has been supported in part by the Collaborative Research Center “Statistical modeling of nonlinear dynamic processes” (SFB 823, Teilprojekt C1) of the German Research Foundation (DFG).
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Dette, H., Guhlich, M. & Neumeyer, N. Testing for additivity in nonparametric quantile regression. Ann Inst Stat Math 67, 437–477 (2015). https://doi.org/10.1007/s10463-014-0461-1
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DOI: https://doi.org/10.1007/s10463-014-0461-1