A Theil-like Class of Inequality Measures, its Asymptotic Normality Theory and Applications

TL;DR

This paper develops a unified asymptotic normality theory for Theil-Like Inequality Measures (TLIM) using empirical process methods, and applies it to data from UEMOA countries.

Contribution

It introduces a comprehensive asymptotic normality framework for TLIM, extending previous case-specific results to a unified approach.

Findings

Finite-distribution asymptotic normality established

Uniform asymptotic normality demonstrated

Applied to UEMOA countries data

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 elements 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.