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The Jackknife Estimate of Variance
Abstract
Tukey's jackknife estimate of variance for a statistic $S(X_1, X_2, \cdots, X_n)$ which is a symmetric function of i.i.d. random variables $X_i$, is investigated using an ANOVA-like decomposition of $S$. It is shown that the jackknife variance estimate tends always to be biased upwards, a theorem to this effect being proved for the natural jackknife estimate of $\operatorname{Var} S(X_1, X_2, \cdots, X_{n-1})$ based on $X_1, X_2, \cdots, X_n$.
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Metadata
- Authors
- Efron, B., & Stein, C.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1981-05-01
- Volume
- 9
- Issue
- 3
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1992068214
- Cited by
- 1,436
- References
- 0
- FWCI
- 10.01
- Type
- journal article
- Language
- en
- Open access
- closed
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