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Journal Articles Journal of Business and Economic Statistics Year : 2015

Goodness of Fit: An Axiomatic Approach


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.


Dates and versions

hal-01456107 , version 1 (03-02-2017)



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