Jackknife Empirical Likelihood-based inference for S-Gini indices

TL;DR

This paper introduces empirical likelihood and jackknife empirical likelihood methods for inference on S-Gini indices, providing confidence intervals and hypothesis tests, with applications to income inequality data.

Contribution

It develops new EL and JEL inference techniques for S-Gini indices, including confidence intervals and hypothesis testing, with theoretical validation and practical application.

Findings

Limiting distributions are Chi-square with one degree of freedom.

Proposed methods outperform bootstrap in simulations.

Application to income data demonstrates practical utility.

Abstract

Widely used income inequality measure, Gini index is extended to form a family of income inequality measures known as Single-Series Gini (S-Gini) indices. In this study, we develop empirical likelihood (EL) and jackknife empirical likelihood (JEL) based inference for S-Gini indices. We prove that the limiting distribution of both EL and JEL ratio statistics are Chi-square distribution with one degree of freedom. Using the asymptotic distribution we construct EL and JEL based confidence intervals for realtive S-Gini indices. We also give bootstrap-t and bootstrap calibrated empirical likelihood confidence intervals for S-Gini indices. A numerical study is carried out to compare the performances of the proposed confidence interval with the bootstrap methods. A test for S-Gini indices based on jackknife empirical likelihood ratio is also proposed. Finally we illustrate the proposed method using an income data.