Goodness of Fit: An Axiomatic Approach

What is it about?

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.

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Why is it important?

The approach helps to check whether parametric specifications of income distributions are in accord with available data. If so, this greatly facilitates analysis of income data, and making appropriate policy decisions.

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