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2015 A significance test for covariates in nonparametric regression
Pascal Lavergne, Samuel Maistre, Valentin Patilea
Electron. J. Statist. 9(1): 643-678 (2015). DOI: 10.1214/15-EJS1005


We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the null hypothesis, so that the curse of dimensionality is mitigated. The test statistic is asymptotically pivotal and the rate of which the test detects local alternatives depends only on the dimension of the covariates under the null hypothesis. We show the validity of wild bootstrap for the test. In small samples, our test is competitive compared to existing procedures.


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Pascal Lavergne. Samuel Maistre. Valentin Patilea. "A significance test for covariates in nonparametric regression." Electron. J. Statist. 9 (1) 643 - 678, 2015.


Published: 2015
First available in Project Euclid: 2 April 2015

zbMATH: 1309.62076
MathSciNet: MR3331853
Digital Object Identifier: 10.1214/15-EJS1005

Primary: 62G08 , 62G10
Secondary: 62G20

Keywords: $U$-statistic , Asymptotic pivotal test statistic , bootstrap , kernel smoothing

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 1 • 2015
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