Asymptotic distributions and performance of empirical skewness measures

A number of skewness measures have been proposed and applied to theoretical distributions. However, the corresponding empirical counterparts have been analyzed only rarely, especially with respect to their asymptotic properties and limit distributions. Six of these empirical measures are considered. After discussing some general properties, the limiting distribution for each measure is derived under weak assumptions. The performance of these estimators is analyzed in simulations using tests and the coverage probabilities of confidence intervals. A particular focus is put on the standardized central third moment as the most popular measure of skewness. Since it turns out to behave poorly, especially when sample sizes are small, the use of alternative and more suitable skewness measures is recommended. A real data application illustrates some of the findings. (C) 2020 Elsevier B.V. All rights reserved.