Order of approximation in the central limit theorem for associated random variables and a moderate deviation result

TL;DR

This paper improves the understanding of the rate of convergence in the central limit theorem for associated stationary random variables and establishes a moderate deviation result, refining previous findings.

Contribution

It provides a new, sharper estimate of the approximation order in the CLT for associated variables and extends the theory with a moderate deviation result, improving upon prior work.

Findings

Enhanced approximation order in the CLT for associated variables

Established a new moderate deviation result

Refined previous theoretical bounds

Abstract

An estimate of the order of approximation in the central limit theorem for strictly stationary associated random variables with finite moments of order q > 2 is obtained. A moderate deviation result is also obtained. We have a refinement of recent results in Cagin et al. (2016). The order of approximation obtained here is an improvement over the corresponding result in Wood (1983).