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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.
Efron et al. (1981) studied this question.