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Local Power Properties of Kernel Based Goodness of Fit Tests

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  • Gouriéroux, Christian
  • Tenreiro, Carlos

Abstract

If (Xi, i[set membership, variant]) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H0: {f=f0}, where f0 is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between fn, a kernel estimator of f, and f0, or between fn and its expected value computed under H0. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071-1095).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 78 (2001)
Issue (Month): 2 (August)
Pages: 161-190

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Handle: RePEc:eee:jmvana:v:78:y:2001:i:2:p:161-190

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Related research

Keywords: goodness of fit tests kernel density estimator integrated square error asymptotic power local alternatives;

References

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  1. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
  2. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
  3. Carlos TENREIRO, 1996. "Tests d'ajustement à une densité fondés sur un estimateur non paramétrique à noyau pour des observations dépendantes," Annales d'Economie et de Statistique, ENSAE, issue 43, pages 129-148.
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Cited by:
  1. Dennis Kristensen, 2010. "Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models," Discussion Papers 10-10, University of Copenhagen. Department of Economics.
  2. Taoufik Bouezmarni & Jeroen V.K. Rombouts & Abderrahim Taamouti, 2011. "Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 275-287, October.
  3. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
  4. 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.

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