The Annals of Statistics

Necessary Conditions for the Bootstrap of the Mean

Evarist Gine and Joel Zinn

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Abstract

It is proved that $EX^2 < \infty$ is necessary for a very mild form of the bootstrap of the mean to work a.s. and that $X$ must be in the domain of attraction of the normal law if a.s. is weakened to "in probability."

Article information

Source
Ann. Statist. Volume 17, Number 2 (1989), 684-691.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347134

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176347134

Mathematical Reviews number (MathSciNet)
MR994259

Zentralblatt MATH identifier
0672.62026

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62F12: Asymptotic properties of estimators 60F05: Central limit and other weak theorems

Keywords
Bootstrap (of the mean) central limit theorem

Citation

Gine, Evarist; Zinn, Joel. Necessary Conditions for the Bootstrap of the Mean. The Annals of Statistics 17 (1989), no. 2, 684--691. doi:10.1214/aos/1176347134. http://projecteuclid.org/euclid.aos/1176347134.


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