 Limit distributions for measures of multivariate skewness and kurtosis based on projectionsL. Baringhaus and N. Henze Journal of Multivariate Analysis, 1991, vol. 38, issue 1, 51-69 Abstract: We derive the asymptotic distributions for measures of multivariate skewness and kurtosis defined by Malkovich and Afifi if the underlying distribution is elliptically symmetric. A key step in the derivation is an approximation by suitable Gaussian processes defined on the surface of the unit d-sphere. It is seen that a test for multivariate normality based on skewness in the sense of Malkovich and Afifi is inconsistent against each fixed elliptically symmetric non-normal distribution provided that a weak moment condition holds. Consistency of a test for multinormality based on kurtosis within the class of elliptically symmetric distributions depends on the fourth moment of the marginal distribution of the standardized underlying law. Our results may also be used to give tests for a special elliptically symmetric type against asymmetry or difference in kurtosis. Keywords: multivariate; skewness; multivariate; kurtosis; test; for; multivariate; normality; elliptically; symmetric; distributions; univariate; projections (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:38:y:1991:i:1:p:51-69 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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