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Parametric versus nonparametric goodness of fit: Another view

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  • Läuter, Henning
  • Nikulin, Michail

Abstract

We consider chi-squared type tests for testing the hypothesis H 0 that a density f of observations X1,..., Xn lies in a parametric class of densities F. We consider a version of chi-squared type test using kernel estimates for the density. The main result is, following Liero, Läuter and Konakov (1998) the derivation of the asymptotic behavior of the power of the test under Pitman and sharp peak type alternatives. The connection of the rate of convergence of these local alternatives, the bandwidth of the kernel estimator, the parametric estimator, the power of the test are studied.

Suggested Citation

  • Läuter, Henning & Nikulin, Michail, 1999. "Parametric versus nonparametric goodness of fit: Another view," SFB 373 Discussion Papers 1999,14, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199914
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    References listed on IDEAS

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    1. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    3. Härdle, W. & Marron, S.J., 1990. "Semiparametric comparison of regression curves," LIDAM Reprints CORE 890, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Konakov, V. & Läuter, H. & Liero, H., 1995. "Nonparametric versus Parametric Goodness of Fit," SFB 373 Discussion Papers 1995,49, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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