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Goodness of Fit: an axiomatic approach

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.
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https://halshs.archives-ouvertes.fr/halshs-00639075
Contributor : Anne Peguin-Feissolle <>
Submitted on : Tuesday, November 8, 2011 - 10:26:50 AM
Last modification on : Wednesday, August 5, 2020 - 3:10:46 AM
Long-term archiving on: : Thursday, February 9, 2012 - 2:30:33 AM

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  • HAL Id : halshs-00639075, version 1

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Frank A. Cowell, Russell Davidson, Emmanuel Flachaire. Goodness of Fit: an axiomatic approach. 2011. ⟨halshs-00639075⟩

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