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Cited by 393

The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.

Bootstrapping General Empirical Measures

Open access
Gine, Evarist, Zinn, Joel·1990·The Annals of Probability
DOI 10.1214/aop/1176990862
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Abstract

It is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions $\mathscr{F}$ and based on a probability measure $P$ holds a.s. if and only if $\mathscr{F} \in \mathrm{CLT}(P)$ and $\int F^2 dP < \infty$, where $F = \sup_{f \in \mathscr{F}}|f|$, and it holds in probability if and only if $\mathscr{F} \in \mathrm{CLT}(P)$. Thus, for a large class of statistics, no local uniformity of the CLT (about $P$) is needed for the bootstrap to work. Consistency of the bootstrap (the bootstrapped law of large numbers) is also characterized. (These results are proved under certain weak measurability assumptions on $\mathscr{F}$.)

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Metadata

Authors
Gine, E., & Zinn, J.
Venue
The Annals of Probability
Publisher
Institute of Mathematical Statistics
Published
1990-04-01
Volume
18
Issue
2
ISSN
0091-1798 (ISSN-L)
DOI
10.1214/aop/1176990862
OpenAlex
W2001288744
Cited by
393
References
16
FWCI
5.11
Type
journal article
Language
en
Open access
bronze

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CoChat. (2026). Citation check: Bootstrapping General Empirical Measures. https://app.cochat.ai/papers/10.1214/aop/1176990862
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Gine, E., & Zinn, J. (1990). Bootstrapping General Empirical Measures. The Annals of Probability. https://doi.org/10.1214/aop/1176990862

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