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August 1998 Empirical Edgeworth expansions for symmetric statistics
Hein Putter, Willem R. van Zwet
Ann. Statist. 26(4): 1540-1569 (August 1998). DOI: 10.1214/aos/1024691253

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.

Citation

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Hein Putter. Willem R. van Zwet. "Empirical Edgeworth expansions for symmetric statistics." Ann. Statist. 26 (4) 1540 - 1569, August 1998. https://doi.org/10.1214/aos/1024691253

Information

Published: August 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0929.62013
MathSciNet: MR1647697
Digital Object Identifier: 10.1214/aos/1024691253

Subjects:
Primary: 62E20, 62G09

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 4 • August 1998
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