We study the asymptotic behavior of Mardia's measure of (sample) multivariate skewness. In the special case of an elliptically symmetric distribution, the limit law is a weighted sum of two independent $\chi^2$-variates. A normal limit distribution arises if the population distribution has positive skewness. These results explain some curiosities in the power performance of a commonly proposed test for multivariate normality based on multivariate skewness.
Publié le : 1992-12-14
Classification:
Multivariate skewness,
test for multivariate normality,
consistency,
elliptically symmetric distributions,
$V$-statistics,
62H15,
62H10
@article{1176348894,
author = {Baringhaus, L. and Henze, N.},
title = {Limit Distributions for Mardia's Measure of Multivariate Skewness},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1889-1902},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348894}
}
Baringhaus, L.; Henze, N. Limit Distributions for Mardia's Measure of Multivariate Skewness. Ann. Statist., Tome 20 (1992) no. 1, pp. 1889-1902. http://gdmltest.u-ga.fr/item/1176348894/