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October, 1995 The Asymptotic Accuracy of the Bootstrap of $U$-Quantiles
Miguel A. Arcones
Ann. Statist. 23(5): 1802-1822 (October, 1995). DOI: 10.1214/aos/1176324324


The order of the Kolmogorov-Smirnov distance for the bootstrap of $U$-quantiles is considered. We observe that the order of the bootstrap of $U$-quantiles depends on the order of the local variance of the first term of the Hoeffding decomposition at the $U$-quantile. This order can be smaller than the order of the bootstrap of quantiles: $U$-quantiles can be smoother than quantiles.


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Miguel A. Arcones. "The Asymptotic Accuracy of the Bootstrap of $U$-Quantiles." Ann. Statist. 23 (5) 1802 - 1822, October, 1995.


Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0845.62035
MathSciNet: MR1370308
Digital Object Identifier: 10.1214/aos/1176324324

Primary: 62E25
Secondary: 60F05 , 62E20

Keywords: $U$-statistic , bootstrap , Edgeworth expansion , empirical process , quantile

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 5 • October, 1995
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