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Local Power Properties of Kernel Based Goodness of Fit Tests

  • Gouriéroux, Christian
  • Tenreiro, Carlos

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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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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  1. 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.
  2. 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.
  3. 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.
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