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Goodness of Fit: an axiomatic approach

Author

Listed:
  • Frank A. Cowell

    () (STICERD - LSE - London School of Economics and Political Science)

  • Russell Davidson

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

  • Emmanuel Flachaire

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

Abstract

An axiomatic approach is used to develop a one-parameter family of measures of divergence between distributions. These measures can be used to perform goodness-of-fit tests with good statistical properties. Asymptotic theory shows that the test statistics have well-defined limiting distributions which are however analytically intractable. A parametric bootstrap procedure is proposed for implementation of the tests. The procedure is shown to work very well in a set of simulation experiments, and to compare favourably with other commonly used goodness-of-fit tests. By varying the parameter of the statistic, one can obtain information on how the distribution that generated a sample diverges from the target family of distributions when the true distribution does not belong to that family. An empirical application analyses a UK income data set.

Suggested Citation

  • Frank A. Cowell & Russell Davidson & Emmanuel Flachaire, 2011. "Goodness of Fit: an axiomatic approach," Working Papers halshs-00639075, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00639075
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00639075
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    References listed on IDEAS

    as
    1. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    2. Amartya Sen, 1976. "Real National Income," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 19-39.
    3. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    4. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 53(3), pages 265-268, December.
    5. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    6. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
    7. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
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    Cited by:

    1. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.

    More about this item

    Keywords

    Goodness of fit; axiomatic approach; measures of divergence; parametric bootstrap;

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