Iterated Jackknives and Two-Sided Variance Inequalities
arXiv:1912.12776 · doi:10.1007/978-3-030-26391-1_4
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.
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