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8 novembre 2011
- ISIDORE Id: 10670/1.000d7f...
- halshs: halshs-00639075
info:eu-repo/semantics/OpenAccess
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Frank A. Cowell et al., « Goodness of Fit: an axiomatic approach », HAL SHS (Sciences de l’Homme et de la Société), ID : 10670/1.000d7f...
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Résumé
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.
