Empirical Edgeworth expansions for symmetric statistics
Hein Putter, Willem R. van Zwet
The Annals of Statistics · 1998 · Volume 26 · Issue 4
Abstract
In this paper the validity of a one-term Edgeworth expansion for Studentized symmetric statistics is proved. We propose jackknife estimates for the unknown constants appearing in the expansion and prove their consistency. As a result we obtain the second-order correctness of the empirical Edgeworth expansion for a very general class of statistics, including $U$-statistics, $L$-statistics and smooth functions of the sample mean. We illustrate the application of the bootstrap in the case of a $U$-statistic of degree two.
Keywords
62E20, 62G09, boot-strap, Edgeworth expansion, Hoeffding’s decomposition, jackknife
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