Abstract
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.
Keywords
Jackknife resamplingMathematicsStatisticsRandom variableDistribution (mathematics)Linear discriminant analysisCombinatoricsApplied mathematicsMathematical analysis
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Publication Info
- Year
- 1979
- Type
- article
- Volume
- 7
- Issue
- 1
- Citations
- 16966
- Access
- Closed
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Cite This
B. Efron
(1979).
Bootstrap Methods: Another Look at the Jackknife.
The Annals of Statistics
, 7
(1)
.
https://doi.org/10.1214/aos/1176344552
Identifiers
- DOI
- 10.1214/aos/1176344552