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Tukey's jackknife estimate of variance for a statistic S (X₁, X₂, , Xₙ) which is a symmetric function of i. i. d. random variables Xᵢ, 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 Var S (X₁, X₂, , X₍-₁) based on X₁, X₂, , Xₙ.
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Efron et al. (Fri,) studied this question.
www.synapsesocial.com/papers/6a0b414d4f5e7da68b2e31e2 — DOI: https://doi.org/10.1214/aos/1176345462
B. Efron
C. Stein
The Annals of Statistics
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