Multivariate skewness and kurtosis measures with an application in ICA

Tõnu Kollo

Journal of Multivariate Analysis, 2008, vol. 99, issue 10, 2328-2338

Abstract: In this paper skewness and kurtosis characteristics of a multivariate p-dimensional distribution are introduced. The skewness measure is defined as a p-vector while the kurtosis is characterized by a pxp-matrix. The introduced notions are extensions of the corresponding measures of Mardia [K.V. Mardia, Measures of multivariate skewness and kurtosis with applications, Biometrika 57 (1970) 519-530] and Mori, Rohatgi & Szekely [T.F. Mori, V.K. Rohatgi, G.J. Szekely, On multivariate skewness and kurtosis, Theory Probab. Appl. 38 (1993) 547-551]. Basic properties of the characteristics are examined and compared with both the above-mentioned results in the literature. Expressions for the measures of skewness and kurtosis are derived for the multivariate Laplace distribution. The kurtosis matrix is used in Independent Component Analysis (ICA) where the solution of an eigenvalue problem of the kurtosis matrix determines the transformation matrix of interest [A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis, Wiley, New York, 2001].

Keywords: 62E20; 62H10; 65C60; Independent; component; analysis; Multivariate; cumulants; Multivariate; kurtosis; Multivariate; moments; Multivariate; skewness (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (34)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00062-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:99:y:2008:i:10:p:2328-2338

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

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
Bibliographic data for series maintained by Catherine Liu ().