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Bandwidth selection for nonparametric kernel testing

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Author Info
Gao, Jiti
Gijbels, Irene

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Abstract

We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed-form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions. For example, when a significance level is given, we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level. Both asymptotic theory and methodology are established. In addition, we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example.

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File URL: http://mpra.ub.uni-muenchen.de/11982/
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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11982.

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Date of creation: Dec 2005
Date of revision: Jun 2007
Publication status: Forthcoming in Journal of the American Statistical Association 4.483(2008): pp. 1-11
Handle: RePEc:pra:mprapa:11982

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Related research
Keywords: Choice of bandwidth parameter; Edgeworth expansion; nonparametric kernel testing; power function; size function;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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  7. S. Chen & W. Härdle & T. Kleinow, . "An Empirical Likelihood Goodness-of-Fit Test for Time Series," Sonderforschungsbereich 373 2001-1, Humboldt Universitaet Berlin.
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  8. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December. [Downloadable!] (restricted)
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  15. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
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  16. Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 73(3), pages 903-948, 05. [Downloadable!] (restricted)
    Other versions:
  17. W. González-Manteiga & R. Cao, 1993. "Testing the hypothesis of a general linear model using nonparametric regression estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 2(1), pages 161-188, December. [Downloadable!] (restricted)
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