Goodness of Fit: An Axiomatic Approach

Frank Cowell (), Russell Davidson and Emmanuel Flachaire

Journal of Business & Economic Statistics, 2015, vol. 33, issue 1, 54-67

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.

Date: 2015
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Working Paper: Goodness of Fit: An Axiomatic Approach (2015)
Working Paper: Goodness of Fit: an axiomatic approach (2011)
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DOI: 10.1080/07350015.2014.922470

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