Goodness of Fit: an axiomatic approach
AbstractAn 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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Date of creation: 08 Nov 2011
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Goodness of fit; axiomatic approach; measures of divergence; parametric bootstrap;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-21 (All new papers)
- NEP-ECM-2011-11-21 (Econometrics)
- NEP-LTV-2011-11-21 (Unemployment, Inequality & Poverty)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826, October.
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- Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
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