Jackknife Empirical Likelihood-based inference for S-Gini indices
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.
Cite
@article{arxiv.1707.04998,
title = {Jackknife Empirical Likelihood-based inference for S-Gini indices},
author = {Sreelakshmi N and Sudheesh K Kattumannil and Rituparna Sen},
journal= {arXiv preprint arXiv:1707.04998},
year = {2024}
}