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Article Dans Une Revue Theoretical Mathematics and Applications Année : 2011

Gram Charlier and Edgeworth expansion for sample variance

Résumé

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 con-vergent. This results can obviously apply to strongly mixing normal process and provide an alternative to the work of Moschopoulos (1985) and Mathai (1982). Mathematics Subject Classification : 62E10, 62E15
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hal-02012464 , version 1 (08-02-2019)

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  • HAL Id : hal-02012464 , version 1

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Eric Benhamou. Gram Charlier and Edgeworth expansion for sample variance. Theoretical Mathematics and Applications, 2011, x (4), pp.1792 - 6939. ⟨hal-02012464⟩
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