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Goodness of Fit: An Axiomatic Approach

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  • Frank A. Cowell
  • Russell Davidson
  • Emmanuel Flachaire
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 favorably 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 analyzes a U.K. income dataset.

Suggested Citation

  • Frank A. Cowell & Russell Davidson & Emmanuel Flachaire, 2015. "Goodness of Fit: An Axiomatic Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 54-67, January.
    • Handle: RePEc:taf:jnlbes:v:33:y:2015:i:1:p:54-67
    DOI: 10.1080/07350015.2014.922470
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    1. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    2. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819, October.
    3. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages 2-18, September.
    4. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications 3 Volume Paperback Set," Cambridge Books, Cambridge University Press, number 9780521581394.
    5. Amartya Sen, 1976. "Real National Income," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 19-39.
    6. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    7. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 53(3), pages 265-268, December.
    8. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833, October.
    9. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    10. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
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    Cited by:

    1. Tsvetana Spasova, 2019. "Regional Income Distribution in the European Union: A Parametric Approach," Research on Economic Inequality, in: What Drives Inequality?, volume 27, pages 1-18, Emerald Group Publishing Limited.
    2. Frank Cowell & Emmanuel Flachaire & Sanghamitra Bandyopadhyay, 2013. "Reference distributions and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(4), pages 421-437, December.
    3. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    4. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "Axiomatic characterization of the χ 2 dissimilarity measure," Working Papers hal-03463741, HAL.

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