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Bootstrap Methods: Another Look at the Jackknife
Open accessAbstract
We discuss the following problem: given a random sample $\mathbf{X} = (X_1, X_2, \cdots, X_n)$ from an unknown probability distribution $F$, estimate the sampling distribution of some prespecified random variable $R(\mathbf{X}, F)$, on the basis of the observed data $\mathbf{x}$. (Standard jackknife theory gives an approximate mean and variance in the case $R(\mathbf{X}, F) = \theta(\hat{F}) - \theta(F), \theta$ some parameter of interest.) A general method, called the "bootstrap," is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.
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“He also establishes that the infinitesimal jackknife (Efron, 1979) consistently estimates the forest variance.”
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Metadata
- Authors
- Efron, B.
- Affiliations
- Stanford University (US)
- Corresponding author
- Efron, B.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1979-01-01
- Volume
- 7
- Issue
- 1
- Pages
- 1-26
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- OpenAlex
- W2117897510
- Cited by
- 17,602
- References
- 14
- Citations by year
- 2026: 865 · 2025: 599 · 2024: 592 · 2023: 654 · 2022: 679 · 2021: 887 · 2020: 890 · 2019: 895 · 2018: 848 · 2017: 720 · 2016: 780 · 2015: 791 · 2014: 838 · 2013: 717 · 2012: 702
- FWCI
- 31.83
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- bootstrapping, jackknife, linearization, linear discriminant analysis, ratio estimation, regression coefficient estimation, nonparametric estimation
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