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Asymptotic theory for statistics based on cumulant vectors with applications
Author(s) -
Rao Jammalamadaka Sreenivasa,
Taufer Emanuele,
Terdik György H.
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12521
Subject(s) - cumulant , mathematics , kurtosis , edgeworth series , skewness , multivariate statistics , asymptotic analysis , asymptotic distribution , elliptical distribution , multivariate normal distribution , statistics , statistical physics , estimator , physics
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.