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arXiv · 1912.12776

Iterated Jackknives and Two-Sided Variance Inequalities

Olivier Bousquet·Christian Houdré
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Abstract

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.

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Olivier Bousquet, Christian Houdré. 2019-12-30. Iterated Jackknives and Two-Sided Variance Inequalities. https://doi.org/10.1007/978-3-030-26391-1_4

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