The Annals of Statistics

Some Asymptotic Theory for the Bootstrap

Peter J. Bickel and David A. Freedman

Full-text: Open access

Abstract

Efron's "bootstrap" method of distribution approximation is shown to be asymptotically valid in a large number of situations, including $t$-statistics, the empirical and quantile processes, and von Mises functionals. Some counter-examples are also given, to show that the approximation does not always succeed.

Article information

Source
Ann. Statist., Volume 9, Number 6 (1981), 1196-1217.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345637

Digital Object Identifier
doi:10.1214/aos/1176345637

Mathematical Reviews number (MathSciNet)
MR630103

Zentralblatt MATH identifier
0449.62034

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation 62G15: Tolerance and confidence regions

Keywords
Bootstrap resampling asymptotic theory

Citation

Bickel, Peter J.; Freedman, David A. Some Asymptotic Theory for the Bootstrap. Ann. Statist. 9 (1981), no. 6, 1196--1217. doi:10.1214/aos/1176345637. https://projecteuclid.org/euclid.aos/1176345637


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