LIMIT DISTRIBUTIONS FOR MARDIA MEASURE OF MULTIVARIATE SKEWNESS

• 成果类型: Article
• 署名作者: BARINGHAUS, L; HENZE, N
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348894
• 发表日期: 1992
• 页码: 1889-1902
• 关键词: robustness; kurtosis; sample

摘要

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 chi2-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 bared on multivariate skewness.