The Annals of Probability

Exchangeably Weighted Bootstraps of the General Empirical Process

Jens Praestgaard and Jon A. Wellner

Full-text: Open access

Abstract

We consider an exchangeably weighted bootstrap of the general function-indexed empirical process. We find sufficient conditions on the bootstrap weights for the central limit theorem to hold for the bootstrapped empirical process, almost surely and in probability. The results resemble those of Gine and Zinn for Efron's bootstrap. As a corollary we obtain a result on the almost sure convergence in distribution of the Efron-bootstrapped empirical process with arbitrary sample size. A large number of bootstrap resampling schemes emerge as special cases of our results.

Article information

Source
Ann. Probab., Volume 21, Number 4 (1993), 2053-2086.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989011

Digital Object Identifier
doi:10.1214/aop/1176989011

Mathematical Reviews number (MathSciNet)
MR1245301

Zentralblatt MATH identifier
0792.62038

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62E20: Asymptotic distribution theory 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)

Keywords
Bootstrap exchangeability empirical process

Citation

Praestgaard, Jens; Wellner, Jon A. Exchangeably Weighted Bootstraps of the General Empirical Process. Ann. Probab. 21 (1993), no. 4, 2053--2086. doi:10.1214/aop/1176989011. https://projecteuclid.org/euclid.aop/1176989011


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