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Iterated Jackknives and Two-Sided Variance Inequalities

Christian Houdré
High Dimensional Probability, vol. VIII (2019), pp. 33-40


We consider the variance of a function of $n$ independent random variables and provide inequalities that generalize previous results obtained for i.i.d. random variables. In particular we obtain upper and lower bounds on the variance based on iterated Jackknife statistics that can be considered as higher-order Efron-Stein inequalities.