A Review on asymptotic normality of sums of associated random variables

Abstract

Association between random variables is a generalization of independence of these random variables. This concept is more and more commonly used in current trends in any research elds in Statistics. In this paper, we proceed to a simple, clear and rigorous introduction to it. We will present the fundamental asymptotic normality theorem on stationary and associated sequences of random variables. A coherent and modern frame is used. This review will be protable to new resarchers in the topic.

Keywords: Positive and Negative Dependence; Association; Central Limit Theorem