Jackknife Empirical Likelihood-based inference for S-Gini indices
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2017
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| _version_ | 1866917677177503744 |
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| author | N, Sreelakshmi Kattumannil, Sudheesh K Sen, Rituparna |
| author_facet | N, Sreelakshmi Kattumannil, Sudheesh K Sen, Rituparna |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1707_04998 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Jackknife Empirical Likelihood-based inference for S-Gini indices N, Sreelakshmi Kattumannil, Sudheesh K Sen, Rituparna Methodology 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. |
| title | Jackknife Empirical Likelihood-based inference for S-Gini indices |
| topic | Methodology |
| url | https://arxiv.org/abs/1707.04998 |