Jackknife empirical likelihood-based inference for S-Gini indices

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...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2021-07, Vol.50 (6), p.1645-1661
Main Authors: Sreelakshmi, N., Kattumannil, Sudheesh K., Sen, Rituparna
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Chi-square test
Confidence intervals
Empirical likelihood
Gini index
Income
Income inequality
Inference
Jackknife empirical likelihood
Likelihood ratio
S-Gini index
Statistical analysis
Statistical methods
Statistical tests
U-statistics
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Summary: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.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2019.1586930