Iterated Jackknives and Two-Sided Variance Inequalities

12/30/2019

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by   Olivier Bousquet, et al.

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We consider the variance of a function of n independent random variables and provide new inequalities which, in particular, extend previous results obtained for symmetric functions in the i.i.d. setting. For instance, we obtain various upper and lower variance bounds based on iterated jackknives statistics that can be considered as generalizations of the Efron-Stein inequality.