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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 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.
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Contributor : Patrice Cacciuttolo <>
Submitted on : Friday, February 3, 2017 - 11:58:20 PM
Last modification on : Wednesday, August 5, 2020 - 3:13:37 AM

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Frank A. Cowell, Russell Davidson, Emmanuel Flachaire. Goodness of Fit: An Axiomatic Approach. Journal of Business and Economic Statistics, Taylor & Francis, 2015, 33 (1), pp.54--67. ⟨10.1080/07350015.2014.922470⟩. ⟨hal-01456107⟩

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