Open Access
November, 1981 On the Asymptotic Accuracy of Efron's Bootstrap
Kesar Singh
Ann. Statist. 9(6): 1187-1195 (November, 1981). DOI: 10.1214/aos/1176345636


In the non-lattice case it is shown that the bootstrap approximation of the distribution of the standardized sample mean is asymptotically more accurate than approximation by the limiting normal distribution. The exact convergence rate of the bootstrap approximation of the distributions of sample quantiles is obtained. A few other convergence rates regarding the bootstrap method are also studied.


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Kesar Singh. "On the Asymptotic Accuracy of Efron's Bootstrap." Ann. Statist. 9 (6) 1187 - 1195, November, 1981.


Published: November, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0494.62048
MathSciNet: MR630102
Digital Object Identifier: 10.1214/aos/1176345636

Primary: 62G05
Secondary: 62G15

Keywords: Berry-Esseen bound , bootstrap , central limit theorem , Edgeworth expansion , lattice distributions , Law of iterated logarithm , Zero-one law

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 6 • November, 1981
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