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

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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.

Integrity signals

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

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Authors: Politis, D. N., & Romano, J. P.
Affiliations: Purdue University West Lafayette (US)
Stanford University (US)
ORCID: Politis, Dimitris N.
Romano, Joseph P.
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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

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The Stationary Bootstrap

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks