On asymptotic behavior of U-statistics for associated random variables

TL;DR

This paper investigates the long-term behavior of U-statistics derived from stationary associated random variables, focusing on kernels with bounded Hardy-Krause variation, to understand their asymptotic properties.

Contribution

It provides new insights into the asymptotic behavior of U-statistics for associated variables with specific kernel variation conditions.

Findings

Established limiting distributions for U-statistics in this setting

Extended existing results to kernels with bounded Hardy-Krause variation

Provided theoretical foundations for analyzing associated random variables

Abstract

Let ${X_n, n \ge 1}$ be a sequence of stationary associated random variables. For such a sequence, we discuss the limiting behavior of U-statistics based on kernels which are of bounded Hardy-Krause variation.