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 $X_1, X_2, \cdots, X_n$.
Citation
B. Efron. C. Stein. "The Jackknife Estimate of Variance." Ann. Statist. 9 (3) 586 - 596, May, 1981. https://doi.org/10.1214/aos/1176345462
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