The Annals of Statistics

The Jackknife Estimate of Variance

B. Efron and C. Stein

Full-text: Open access

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 $X_1, X_2, \cdots, X_n$.

Article information

Source
Ann. Statist. Volume 9, Number 3 (1981), 586-596.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176345462

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176345462

Mathematical Reviews number (MathSciNet)
MR615434

Zentralblatt MATH identifier
0481.62035

Subjects
Primary: 62G05: Estimation

Keywords
Jackknife variance estimation ANOVA decomposition bootstrap $U$ statistics

Citation

Efron, B.; Stein, C. The Jackknife Estimate of Variance. Ann. Statist. 9 (1981), no. 3, 586--596. doi:10.1214/aos/1176345462. http://projecteuclid.org/euclid.aos/1176345462.


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