The Annals of Statistics

Empirical Edgeworth expansions for symmetric statistics

Hein Putter and Willem R. van Zwet

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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.

Article information

Source
Ann. Statist., Volume 26, Number 4 (1998), 1540-1569.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691253

Digital Object Identifier
doi:10.1214/aos/1024691253

Mathematical Reviews number (MathSciNet)
MR1647697

Zentralblatt MATH identifier
0929.62013

Subjects
Primary: 62E20: Asymptotic distribution theory 62G09: Resampling methods

Keywords
Edgeworth expansion Hoeffding’s decomposition jackknife boot-strap

Citation

Putter, Hein; van Zwet, Willem R. Empirical Edgeworth expansions for symmetric statistics. Ann. Statist. 26 (1998), no. 4, 1540--1569. doi:10.1214/aos/1024691253. https://projecteuclid.org/euclid.aos/1024691253


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References

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