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Research Report SRR95-040
Comparisons of variance estimators and their effects for studentized
U statistics
Yoshihiko Maesono
Abstract:
We obtain approximations of several variance estimators of
U-statistics
and discuss effects for studentizations via Edgeworth expansions. In
this paper we obtain asymptotic representations of jackknife, unbiased
and Sen's (1960) variance estimators and using the representations we
establish the Edgeworth expansions of studentized U-statistics
with
remainder term o(n-1). We also show that
Hinkley's (1978) corrected
jackknife estimator coincides the unbiased variance estimator until the
order op(n-1).
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