Iterated Jackknives and Two-Sided Variance Inequalities
Statistics Theory
2020-01-01 v1 Probability
Statistics Theory
Abstract
We consider the variance of a function of 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.
Cite
@article{arxiv.1912.12776,
title = {Iterated Jackknives and Two-Sided Variance Inequalities},
author = {Olivier Bousquet and Christian Houdré},
journal= {arXiv preprint arXiv:1912.12776},
year = {2020}
}
Comments
This paper has appeared in High Dimensional Probability VIII, Part of the Progress in Probability book series (PRPR, volume 74), Pages 33-40. Some typos have been corrected and slight corrections made