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December, 1992 Limit Distributions for Mardia's Measure of Multivariate Skewness
L. Baringhaus, N. Henze
Ann. Statist. 20(4): 1889-1902 (December, 1992). DOI: 10.1214/aos/1176348894

Abstract

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.

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L. Baringhaus. N. Henze. "Limit Distributions for Mardia's Measure of Multivariate Skewness." Ann. Statist. 20 (4) 1889 - 1902, December, 1992. https://doi.org/10.1214/aos/1176348894

Information

Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0767.62041
MathSciNet: MR1193317
Digital Object Identifier: 10.1214/aos/1176348894

Subjects:
Primary: 62H15
Secondary: 62H10

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 4 • December, 1992
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