Bootstrap for U-Statistics: A new approach

TL;DR

This paper introduces a novel bootstrap method for U-statistics that combines bootstrap and subsampling techniques, demonstrating its consistency and favorable finite sample performance.

Contribution

It proposes an alternative bootstrap approach for U-statistics, bridging bootstrap and subsampling, with proven consistency and improved finite sample properties.

Findings

The new method is consistent for dependent data.

Simulation studies show improved finite sample performance.

The approach offers a practical alternative to traditional bootstrap methods.

Abstract

Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the statistic. We suggest an alternative approach of getting a bootstrap version of U-statistics, which can be described as a compromise between bootstrap and subsampling. We will show the consistency of the new method and compare its finite sample properties in a simulation study.