The Annals of Statistics

On the Asymptotic Accuracy of Efron's Bootstrap

Kesar Singh

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Abstract

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.

Article information

Source
Ann. Statist., Volume 9, Number 6 (1981), 1187-1195.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345636

Digital Object Identifier
doi:10.1214/aos/1176345636

Mathematical Reviews number (MathSciNet)
MR630102

Zentralblatt MATH identifier
0494.62048

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G15: Tolerance and confidence regions

Keywords
Bootstrap Berry-Esseen bound lattice distributions central limit theorem law of iterated logarithm zero-one law Edgeworth expansion

Citation

Singh, Kesar. On the Asymptotic Accuracy of Efron's Bootstrap. Ann. Statist. 9 (1981), no. 6, 1187--1195. doi:10.1214/aos/1176345636. https://projecteuclid.org/euclid.aos/1176345636


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