On limiting distribution of U-statistics based on associated random variables

TL;DR

This paper establishes conditions under which U-statistics derived from stationary associated random variables follow a central limit theorem, focusing on differentiable kernels of degree two or higher and exploring applications.

Contribution

It introduces new conditions for CLT applicability to U-statistics based on associated variables, extending previous results to differentiable kernels of degree two or more.

Findings

Central limit theorem holds under new conditions for associated variables.

Results apply to U-statistics with differentiable kernels of degree two or higher.

Includes applications demonstrating the theoretical findings.

Abstract

Let $\{X_n, n \ge 1\}$ be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on $\{X_n, n \ge 1\}$ holds. We look at U-statistics based on differentiable kernels of degree 2 and above. We also discuss some applications.