Expansions for multivariate densities

The Gram–Charlier and Edgeworth series are expansions of probability distribution in terms of its cumulants. The expansions for the multivariate case have not been fully explored. This paper aims to develop the multivariate Gram–Charlier series by Woodroofe–Stein’s identity, and improve its approxim...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2015-12, Vol.167, p.174-181
Main Author: Weng, Ruby C.
Format: Article
Language:English
Subjects:
Edgeworth series
Gram–Charlier series
Hermite polynomials
Woodroofe–Stein’s identity
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Summary:The Gram–Charlier and Edgeworth series are expansions of probability distribution in terms of its cumulants. The expansions for the multivariate case have not been fully explored. This paper aims to develop the multivariate Gram–Charlier series by Woodroofe–Stein’s identity, and improve its approximation property by using the scaled normal density and Hermite polynomials. The series are useful to reconstruct the probability distribution from measurable higher moments. •This paper developed the multivariate Gram–Charlier series by Woodroofe–Stein’s identity.•This paper proposed a modified series for better approximation property.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2015.05.001