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Biometrika 1981 68(3):589-599; doi:10.1093/biomet/68.3.589
© 1981 by Biometrika Trust
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Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods

BRADLEY EFRON

Department of Statistics, Stanford University

We discuss several nonparametric methods for attaching a standard error to a point estimate: the jackknife, the bootstrap, half-sampling, subsampling, balanced repeated replications, the infinitesimal jackknife, influence function techniques and the delta method. The last three methods are shown to be identical. All the methods derive from the same basic idea, which is also the idea underlying the common parametric methods. Extended numerical comparisons are made for the special case of the correlation coefficient.

Key Words: Balanced repeated replications • Bootstrap • Delta method • Half-sampling • Jackknife • Infinitesimal jackknife • Influence function


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