General Central Limit Theorems for Associated Sequences

TL;DR

This paper develops general central limit theorems for associated sequences of random variables, extending existing results, clarifying assumptions, and providing a comprehensive comparison with previous CLTs.

Contribution

It introduces new CLTs for associated sequences under various moment conditions and completes an important existing theorem by filling a missing assumption.

Findings

Established a Lyapounov-Feller-Levy type CLT for associated sequences

Provided specific CLTs based on different moment conditions

Compared new CLTs with existing results, highlighting improvements

Abstract

In this paper, we provide general central limit theorems (CLT's) for associated random variables (rv's) following the approaches used by Newman (1980) and Olivera et al.(2012). Given some assumptions, a Lyapounov-Feller-Levy type theorem is stated. We next specify different particular CLT versions of associated sequences based on moment conditions. A comparison study with available CTL's is performed. As a by-product, we complete an important available theorem where an assumption was missing.