Asymptotic mean square errors of variance estimators and their Edgeworth expansions

Research Report SRR96-001

Asymptotic mean square errors of variance estimators and their Edgeworth expansions

Yoshihiko Maesono

Abstract: In this paper we study variance estimators for a class of U-statistics. We obtain asymptotic representations of jackknife, Hinkely's (1978) corrected jackknife, unbiased, Sen's (1960) and new variance estimators. And we investigate asymptotic mean square errors of them, theoretically. The Edgeworth expansions of the estimators with remainder term o(n^-1) are also established. We show that the normalized Hinkley's corrected estimator coincides the normalized unbiased estimator until the order n^-½o_p(n^-1).

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