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October 2001 Significance testing in nonparametric regression based on the bootstrap
Miguel A. Delgado, Wenceslao González Manteiga
Ann. Statist. 29(5): 1469-1507 (October 2001). DOI: 10.1214/aos/1013203462


This paper proposes a test for selecting explanatory variables in nonparametric regression. The test does not need to estimate the conditional expectation function given all the variables, but only those which are significant under the null hypothesis. This feature is computationally convenient and solves, in part, the problem of the “curse of dimensionality” when selecting regressors in a nonparametric context. The proposed test statistic is based on functionals of a $U$-process. Contiguous alternatives, converging to the null at a rate $n^{-1/2}$ can be detected. The asymptotic null distribution of the statistic depends on certain features of the data generating process,and asymptotic tests are difficult to implement except in rare circumstances. We justify the consistency of two easy to implement bootstrap tests which exhibit good level accuracy for fairly small samples, according to the reported Monte Carlo simulations. These results are also applicable to test other interesting restrictions on nonparametric curves, like partial linearity and conditional independence.


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Miguel A. Delgado. Wenceslao González Manteiga. "Significance testing in nonparametric regression based on the bootstrap." Ann. Statist. 29 (5) 1469 - 1507, October 2001.


Published: October 2001
First available in Project Euclid: 8 February 2002

zbMATH: 1043.62032
MathSciNet: MR1873339
Digital Object Identifier: 10.1214/aos/1013203462

Primary: 62G07 , 62G09 , 62G10

Keywords: higher order kernels , Nonparametric regression , restrictions on nonparametric curves , selection of variables , U-processes , wild bootstrap

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 5 • October 2001
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