Goodness-of-fit tests based on a robust measure of skewness

In this paper we propose several goodness-of-fit tests based on robust measures of skewness and tail weight. They can be seen as generalisations of the Jarque-Bera test (Bera and Jarque in Econ Lett 7:313-318, 1981) based on the classical skewness and kurtosis, and as an alternative to the approach of Moors et al. (Stat Neerl 50:417-430, 1996) using quantiles. The power values and the robustness properties of the different tests are investigated by means of simulations and applications on real data. We conclude that MC-LR, one of our proposed tests, shows the best overall power and that it is moderately influenced by outlying values.