English

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 nn 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.

Keywords

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

R2 v1 2026-06-23T12:58:39.520Z