We consider two measures of right/left/overall kurtosis which are based on a recent interpretation of kurtosis as inequality at either side of the median. We derive the symmetric influence functions of these measures and discuss their sampling properties by a simulation-based approach. Bootstrap confidence intervals are constructed for small and medium sample sizes. Compared to the standardized fourth moment coefficient (conventional kurtosis), the two measures are shown to provide both a more reliable and a more sophisticated picture of the kurtosis risk embedded in a dataset.
Fiori, A. (2010). Two kurtosis measures in a simulation study. In Proceedings in Computational Statistics 2010 (pp.1007-1014). Physica-Verlag, Springerlink.
Two kurtosis measures in a simulation study
FIORI, ANNA MARIA
2010
Abstract
We consider two measures of right/left/overall kurtosis which are based on a recent interpretation of kurtosis as inequality at either side of the median. We derive the symmetric influence functions of these measures and discuss their sampling properties by a simulation-based approach. Bootstrap confidence intervals are constructed for small and medium sample sizes. Compared to the standardized fourth moment coefficient (conventional kurtosis), the two measures are shown to provide both a more reliable and a more sophisticated picture of the kurtosis risk embedded in a dataset.
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