标题： 迭代Jackknives与双侧方差不等式 显示英文标题

标题： Iterated Jackknives and Two-Sided Variance Inequalities

摘要： 我们研究了关于$n$个独立随机变量的函数的方差，并给出了新的不等式，特别是推广了之前在独立同分布（i.i.d.）设定下针对对称函数得到的结果。 例如，我们得到了基于迭代刀切法统计量的各种上下方差界，这些可以被视为对Efron-Stein不等式的推广。 显示英文摘要

摘要： 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.