标题： 泛函的链式法则及其对矩函数的应用 显示英文标题

标题： The chain rule for functionals with applications to functions of moments

摘要： 复合函数求导的链式法则被推广到统计泛函函数的情形，并用于获得样本矩函数的累积量、分布和分位数的近似值，从而得到函数关于样本矩的三阶置信区间以及降低偏差的估计。 作为例子，我们给出了正态样本标准化偏度的分布，其中 $O(n^{-2})$ 表示精度，$n$ 表示样本大小。 显示英文摘要

摘要： The chain rule for derivatives of a function of a function is extended to a function of a statistical functional, and applied to obtain approximations to the cumulants, distribution and quantiles of functions of sample moments, and so to obtain third order confidence intervals and estimates of reduced bias for functions of moments. As an example we give the distribution of the standardized skewness for a normal sample to magnitude $O(n^{-2})$, where $n$ is the sample size.