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Goodness of Fit: An Axiomatic Approach

Listed author(s):
  • Frank A. Cowell
  • Russell Davidson
  • Emmanuel Flachaire

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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File URL: http://hdl.handle.net/10.1080/07350015.2014.922470
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Article provided by Taylor & Francis Journals in its journal Journal of Business & Economic Statistics.

Volume (Year): 33 (2015)
Issue (Month): 1 (January)
Pages: 54-67

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Handle: RePEc:taf:jnlbes:v:33:y:2015:i:1:p:54-67
DOI: 10.1080/07350015.2014.922470
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  1. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
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