On the Edgeworth expansions for functionals of U statistics

Research Report SRR95-015

On the Edgeworth expansions for functionals of U statistics

Yoshihiko Maesono

Abstract: We obtain approximations of standardized and studentized functionals of U-statistics. And under the conditions that (4+\epsilon)th moment of the kernel exists and that the conditional distribution of the kernel is non-lattice, we derive Edgeworth expansions of the both functional with remainder term o(n^-½). The expansions are obtained as explicit forms. We also discuss about the estimation of the standard error, which is an example of the functionals of U-statistics.

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