A Treatment of Multivariate Skewness, Kurtosis, and Related Statistics

This paper gives a unified treatment of the limit laws of different measures of multivariate skewness and kurtosis which are related to components of Neymanʹs smooth test of fit for multivariate normality. The results are also applied to other multivariate statistics which are built up in a similar way as the smooth components. Special emphasis is given to the case that the underlying distribution is elliptically symmetric.