Jackknife empirical likelihood-based inference for S-Gini indices

Abstract

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