Afrika Statistika

A Theil-like class of inequality measures, its asymptotic normality theory and applications

Pape Djiby Mergane, Tchilabalo Abozou Kpanzou, Ba Diam, and Gane Samb Lo

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Abstract

In this paper, we consider a coherent theory about the asymptotic representations for a family of inequality indices called Theil-Like Inequality Measures $(TLIM)$, within a Gaussian field. The theory uses the functional empirical process approach. We provide the inite-distribution and uniform asymptotic normality of the element of the TLIM class in a unified approach rather than in a case by case one. The results are then applied to some UEMOA countries databases.

Résumé

Dans cet article, nous présentons une théorie cohérente de représentations asymptotiques d'une famille de mesures d'inégalité dénommée $TLIM$ dans un champ gaussien précis. Notre méthode est fondée sur le processus empirique fonctionnel. Nous tirons de la représentation asymptotique les limites en distribution des estimateurs plug-in des membres de la famille en dimension finie.Les résultats sont ensuite appliqués à des données issues des pays de l'UEMOA.

Article information

Source
Afr. Stat., Volume 13, Number 3 (2018), 1699-1715.

Dates
First available in Project Euclid: 12 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.as/1544583711

Digital Object Identifier
doi:10.16929/as/1699.129

Mathematical Reviews number (MathSciNet)
MR3887179

Zentralblatt MATH identifier
07003212

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties 62G07: Density estimation 91B82: Statistical methods; economic indices and measures 62P20: Applications to economics [See also 91Bxx]

Keywords
Inequality measure Asymptotic behaviour Asymptotic representations functional empirical process

Citation

Mergane, Pape Djiby; Kpanzou, Tchilabalo Abozou; Diam, Ba; Lo, Gane Samb. A Theil-like class of inequality measures, its asymptotic normality theory and applications. Afr. Stat. 13 (2018), no. 3, 1699--1715. doi:10.16929/as/1699.129. https://projecteuclid.org/euclid.as/1544583711


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