Convergence of the empirical two-sample $U$-statistics with $\beta$-mixing data

TL;DR

This paper studies the convergence behavior of empirical two-sample U-statistics when applied to strictly stationary data exhibiting beta-mixing, providing theoretical insights and practical applications.

Contribution

It extends the understanding of U-statistics convergence to beta-mixing data and demonstrates their application in statistical analysis.

Findings

Established convergence in Skorohod spaces for beta-mixing data

Provided an application demonstrating the utility of the convergence results

Extended theoretical framework for U-statistics with dependent data

Abstract

We consider the empirical two-sample $U$-statistic with strictly $\beta$-mixing strictly stationary data and inverstigate its convergence in Skorohod spaces. We then provide an application of such convergence.