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Cited by 2,649Statistical Methods and InferenceProbability and Statistical ResearchMarkov Chains and Monte Carlo Methods

The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.

The Stationary Bootstrap

Politis, Dimitris N., Romano, Joseph P.·1994·Journal of the American Statistical Association
DOI 10.1080/01621459.1994.10476870
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Abstract

This article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations. Previously, a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m-dimensional joint distribution of m consecutive observations, where m is fixed. This procedure has been generalized by constructing a “blocks of blocks” resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole (i.e., infinite-dimensional) joint distribution of the stationary sequence of observations. These methods share the construction of resampling blocks of observations to form a pseudo-time series, so that the statistic of interest may be recalculated based on the resampled data set. But in the context of applying this method to stationary data, it is natural to require the resampled pseudo-time series to be stationary (conditional on the original data) as well. Although the aforementioned procedures lack this property, the stationary procedure developed here is indeed stationary and possesses other desirable properties. The stationary procedure is based on resampling blocks of random length, where the length of each block has a geometric distribution. In this article, fundamental consistency and weak convergence properties of the stationary resampling scheme are developed.

Overview

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Crossref · 10.1080/01621459.1994.10476870

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Citations

Cites

Show all 27 references

Research works printed but not linked: 4

  1. 10.1080/00401706.1992.10484950 · DOI
  2. Liu R. Y., 1992, Exploring the Limits of Bootstrap
  3. Politis D., Computing Science and Statistics, Proceedings of the 22nd Symposium on the Interface, 98
  4. Politis D., 1992, Exploring the Limits of Bootstrap, 263

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Metadata

Authors
Politis, D. N., & Romano, J. P.
Affiliations
  • Purdue University West Lafayette (US)
  • Stanford University (US)
ORCID
Venue
Journal of the American Statistical Association
Publisher
Informa UK Limited
Published
1994-12
Volume
89
Issue
428
Pages
1303-1313
ISSN
  • 0162-1459 (ISSN-L)
  • 1537-274X
DOI
10.1080/01621459.1994.10476870
OpenAlex
W2076396344
Cited by
2,649
References
27
Citations by year
2026: 279 · 2025: 137 · 2024: 113 · 2023: 108 · 2022: 102 · 2021: 124 · 2020: 136 · 2019: 117 · 2018: 117 · 2017: 129 · 2016: 125 · 2015: 120 · 2014: 119 · 2013: 117 · 2012: 130
FWCI
9.25
Type
journal article
Language
en
Open access
closed
Locations
  • Journal of the American Statistical Association (publishedVersion)
  • Helmholtz Centre for Ocean Research Kiel (GEOMAR) (acceptedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
  • Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
Keywords
stationary bootstrap, resampling, standard errors, confidence regions, geometric distribution, consistency, weak convergence, infinite-dimensional parameters, block bootstrap

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