Conditional Delta-Method for Resampling Empirical Processes in Multiple Sample Problems

TL;DR

This paper develops a general conditional delta-method for resampling empirical processes in multiple sample problems, enhancing the analysis of bootstrap and permutation methods for statistical inference.

Contribution

It introduces a broad conditional delta-method applicable to various resampling procedures in multiple sample settings, filling a gap in existing theoretical tools.

Findings

Provides a unified framework for conditional delta-methods

Demonstrates application in multiple sample resampling scenarios

Enhances understanding of finite sample properties of resampling methods

Abstract

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.