Goodness of Fit: An Axiomatic Approach

Frank A. Cowell, Russell Davidson, Emmanuel Flachaire
2015 Journal of business & economic statistics  
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
more » ... on 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.
doi:10.1080/07350015.2014.922470 fatcat:mdb33awswngppc6radm3juihyu