Goodness of Fit: an axiomatic approach

Frank A. Cowell (1) , Russell Davidson (2) , Emmanuel Flachaire (2)

1 STICERD
2 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

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.

Mots clés: Goodness of fit; axiomatic approach; measures of divergence; parametric bootstrap

Domaines: Economies et finances

Frank A. Cowell, Russell Davidson, Emmanuel Flachaire. Goodness of Fit: an axiomatic approach. 2011. ⟨halshs-00639075⟩