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Gram Charlier and Edgeworth expansion for sample variance

Benhamou, Eric (2018), Gram Charlier and Edgeworth expansion for sample variance, Theoretical Mathematics and Applications, 8, 4, p. 17-31

Type
Article accepté pour publication ou publié
Date
2018
Journal name
Theoretical Mathematics and Applications
Volume
8
Number
4
Publisher
Scienpress
Pages
17-31
Metadata
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Author(s)
Benhamou, Eric
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
In this paper, we derive a valid Edgeworth expansions for the Bessel corrected empirical variance when data are generated by a strongly mixing process whose distribution can be arbitrarily. The constraint of strongly mixing process makes the problem not easy. Indeed, even for a strongly mixing normal process, the distribution is unknown. Here, we do not assume any other assumption than a sufficiently fast decrease of the underlying distribution to make the Edgeworth expansion convergent. This results can obviously apply to strongly mixing normal process and provide an alternative to the work of Moschopoulos (1985) and Mathai (1982).
Subjects / Keywords
sample variance; Edgeworth expansion