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Breaking the curse of dimensionality in nonparametric testing

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  • Lavergne, Pascal
  • Patilea, Valentin

Abstract

For tests based on nonparametric methods, power crucially depends on the dimension of theconditioning variables, and specifically decreases with this dimension. This is known as the“curse of dimensionality." We propose a new general approach to nonparametric testing inhigh dimensional settings and we show how to implement it when testing for a parametricregression. The resulting test behaves against directional local alternatives almost as if thedimension of the regressors was one. It is also almost optimal against classes of onedimensionalalternatives for a suitable choice of the smoothing parameter. A simulationstudy shows that it outperforms the standard test by Zheng (1996).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 143 (2008)
Issue (Month): 1 (March)
Pages: 103-122

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Handle: RePEc:eee:econom:v:143:y:2008:i:1:p:103-122

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Web page: http://www.elsevier.com/locate/jeconom

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References

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Citations

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Cited by:
  1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 361-411, September.
  2. Pascal Lavergne & Valentin Patilea, 2007. "One for All and All for One : Regression Checks with Many Regressors”," Working Papers 2007-12, Centre de Recherche en Economie et Statistique.
  3. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
  4. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.

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