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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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 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.

Résumé

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

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

Dates
First available in Project Euclid: 22 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.as/1461355419

Digital Object Identifier
doi:10.16929/as/2016.855.79

Zentralblatt MATH identifier
1342.60002

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

Keywords
Positive and Negative Dependence Association Central Limit Theorem

Citation

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. https://projecteuclid.org/euclid.as/1461355419


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