Afrika Statistika

A review on asymptotic normality of sums of associated random variables

LO GANE SAMB, Sangare HAROUNA, and Cheikhna Hamallah NDIAYE

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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 fields 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 profitable to new researchers in the topic.


Le concept de variables aléatoires associées est une généralisation de l'indépendance entre variables aléatoires. Il devient de plus en plus important dans les probabilités et les applications statistiques de tous les jours. Dans ce papier, nous introduisons à ce concept et présentons le théorème fondamental de la normalité asymptotique de sommes partielles d'une suite stationnaire de variables aléatoires associées. Nous utilisons un cadre moderne et cohérent qui sera profitable aux chercheurs débutants dans ce domaine.

Article information

Afr. Stat., Volume 11, Number 1 (2016), 855-867.

First available in Project Euclid: 22 April 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 62G20: Asymptotic properties 62H20: Measures of association (correlation, canonical correlation, etc.)

Positive and Negative Dependence Association Central Limit Theorem


GANE SAMB, LO; HAROUNA, Sangare; NDIAYE, Cheikhna Hamallah. A review on asymptotic normality of sums of associated random variables. Afr. Stat. 11 (2016), no. 1, 855--867. doi:10.16929/as/2016.855.79.

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