Goodness of Fit: an axiomatic approach

Frank Cowell (), Russell Davidson and Emmanuel Flachaire

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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.

Keywords: Goodness of fit; axiomatic approach; measures of divergence; parametric bootstrap (search for similar items in EconPapers)
Date: 2011-11-08
New Economics Papers: this item is included in nep-ecm and nep-ltv
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00639075
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Citations: View citations in EconPapers (4)

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Working Paper: Goodness of Fit: An Axiomatic Approach (2015)
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