Gram Charlier and Edgeworth Expansion for Sample Variance.

Summary 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.