IJPAM: Volume 25, No. 3 (2005)
OF MULTIVARIATE KURTOSIS IN
ELLIPTICAL DISTRIBUTIONS
Department of Mathematical Information Science
Tokyo University of Science
1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, JAPAN
e-mails: j1102704@ed.kagu.tus.ac.jp, a1102704@rs.kagu.tus.ac.jp
Abstract.In this paper, we consider the estimation of the kurtosis parameter
in elliptical distributions. The consistent estimators based on measures of
multivariate kurtosis independently defined by Mardia [5] and Srivastava
[7] are presented. In order to investigate accuracy of estimations,
asymptotic expansions of the expectation and the asymptotic variance of the
estimators are derived by a perturbation method under elliptical populations.
Some numerical examples obtained by Monte Carlo simulation for some selected
parameters are also provided.
Received: November 3, 2005
AMS Subject Classification: 62H10, 62E20, 62F12
Key Words and Phrases: asymptotic expansion, consistent estimator, elliptical distribution, kurtosis parameter, moment parameter, perturbation method
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 3
