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May, 1981 The Jackknife Estimate of Variance
B. Efron, C. Stein
Ann. Statist. 9(3): 586-596 (May, 1981). DOI: 10.1214/aos/1176345462


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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B. Efron. C. Stein. "The Jackknife Estimate of Variance." Ann. Statist. 9 (3) 586 - 596, May, 1981.


Published: May, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0481.62035
MathSciNet: MR615434
Digital Object Identifier: 10.1214/aos/1176345462

Primary: 62G05

Keywords: $U$ statistics , ANOVA decomposition , bootstrap , jackknife , variance estimation

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 3 • May, 1981
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