Journal
SCANDINAVIAN JOURNAL OF STATISTICS
Volume 48, Issue 2, Pages 708-728Publisher
WILEY
DOI: 10.1111/sjos.12521
Keywords
elliptically symmetric distributions; Gram– Charlier expansion; multivariate cumulants; multivariate skewness and kurtosis
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Funding
- European Union
- European Social Fund [EFOP3.6.2-16-2017-00015]
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Explicit formulas for the asymptotic covariances of cumulant vectors of the third and the fourth order are provided for any given multivariate distribution, along with general expressions for cumulants of elliptically symmetric multivariate distributions, allowing extension of existing results and obtaining practical expressions.
For any given multivariate distribution, explicit formulae for the asymptotic covariances of cumulant vectors of the third and the fourth order are provided here. General expressions for cumulants of elliptically symmetric multivariate distributions are also provided. Utilizing these formulae one can extend several results currently available in the literature, as well as obtain practically useful expressions in terms of population cumulants, and computational formulae in terms of commutator matrices. Results are provided for both symmetric and asymmetric distributions, when the required moments exist. New measures of skewness and kurtosis based on distinct elements are discussed, and other applications to independent component analysis and testing are considered.
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