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March, 1991 On the Edgeworth Expansion and the Bootstrap Approximation for a Studentized $U$-Statistic
R. Helmers
Ann. Statist. 19(1): 470-484 (March, 1991). DOI: 10.1214/aos/1176347994

Abstract

The asymptotic accuracy of the estimated one-term Edgeworth expansion and the bootstrap approximation for a Studentized $U$-statistic is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of a Studentized $U$-statistic than the normal approximation. The conditions needed to obtain these results are weak moment assumptions on the kernel $h$ of the $U$-statistic and a nonlattice condition for the distribution of $g(X_1) = E\lbrack h(X_1, X_2) \mid X_1\rbrack$. As an application improved Edgeworth and bootstrap based confidence intervals for the mean of a $U$-statistic are obtained.

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R. Helmers. "On the Edgeworth Expansion and the Bootstrap Approximation for a Studentized $U$-Statistic." Ann. Statist. 19 (1) 470 - 484, March, 1991. https://doi.org/10.1214/aos/1176347994

Information

Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0734.62049
MathSciNet: MR1091863
Digital Object Identifier: 10.1214/aos/1176347994

Subjects:
Primary: 62E20
Secondary: 60F05, 62G05

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 1 • March, 1991
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