The Jackknife Estimate of Variance
Efron, B. ; Stein, C.
Ann. Statist., Tome 9 (1981) no. 1, p. 586-596 / Harvested from Project Euclid
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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 $X_1, X_2, \cdots, X_n$.
Publié le : 1981-05-14
Classification:  Jackknife,  variance estimation,  ANOVA decomposition,  bootstrap,  $U$ statistics,  62G05 
@article{1176345462,
     author = {Efron, B. and Stein, C.},
     title = {The Jackknife Estimate of Variance},
     journal = {Ann. Statist.},
     volume = {9},
     number = {1},
     year = {1981},
     pages = { 586-596},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176345462}
}

Efron, B.; Stein, C. The Jackknife Estimate of Variance. Ann. Statist., Tome 9 (1981) no. 1, pp.  586-596. http://gdmltest.u-ga.fr/item/1176345462/