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

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 finite-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. A Theil-like class of inequality measures, its asymptotic normality theory and applications 1700 Résumé. (French) 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 appliquésà des données issues des pays de l'UEMOA.

On the Influence Function for the Theil-Like Class of Inequality Measures

“…This is exactly the case from the asymptotic normality of the plug-in estimator as established in Theorem 2 in [23].…”

“…I this paper, we studied the Theil-like family of inequality measures introduced in [23]. Following the paper on the asymptotic finitedistribution normality, we focus on the IF of that family.…”