## The Annals of Statistics

### 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 $X_1, X_2, \cdots, X_n$.

#### Article information

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

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176345462

Digital Object Identifier
doi:10.1214/aos/1176345462

Mathematical Reviews number (MathSciNet)
MR615434

Zentralblatt MATH identifier
0481.62035

JSTOR