The functional delta-method has a wide range of applications in statistics. Applications on functionals of empirical processes yield various limit results for classical statistics. To improve the finite sample properties of statistical inference procedures that are based on the limit results, resampling procedures such as random permutation and bootstrap methods are a popular solution. In order to analyze the behaviour of the functionals of the resampling empirical processes, corresponding conditional functional delta-methods are desirable. While conditional functional delta-methods for some special cases already exist, there is a lack of more general conditional functional delta-methods for resampling procedures for empirical processes, such as the permutation and pooled bootstrap method. This gap is addressed in the present paper. Thereby, a general multiple sample problem is considered. The flexible application of the developed conditional delta-method is shown in various relevant examples.

翻译：函数Delta方法在统计学中具有广泛的应用。将其应用于经验过程的泛函，可推导出经典统计量的各种极限结果。为了改进基于这些极限结果的统计推断程序在有限样本下的性质，重抽样程序（如随机置换和自助法）是一种流行的解决方案。为了分析重抽样经验过程的泛函行为，需要相应的条件函数Delta方法。虽然针对某些特殊情况的条件函数Delta方法已经存在，但对于经验过程的重抽样程序（如置换法和合并自助法），仍缺乏更一般的条件函数Delta方法。本文旨在填补这一空白。为此，我们考虑了一个一般的多样本问题。并通过多个相关示例展示了所开发的条件Delta方法的灵活应用。