Two Tunable Gini-Type Measures with U-Statistic Estimation: Theory, Simulation, and an Empirical Application to GDP per Capita in the Americas
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914541229572096 |
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| author | Vila, Roberto Saulo, Helton |
| author_facet | Vila, Roberto Saulo, Helton |
| contents | We introduce two families of inequality measures, $G_p$ and $H_q$, that converge to the classical Gini coefficient as $p,q\to\infty$. The tuning parameters $p>1$ and $q>0$ regulate the influence of disparities between observations. For each index we derive closed-form $U$-statistic plug-in estimators and establish strong consistency and asymptotic normality under mild moment conditions. A Monte Carlo study assesses finite-sample behavior across $(n,p,q)$, and an empirical illustration with GDP per capita in the Americas shows how the tuning parameters influence the measure of inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two Tunable Gini-Type Measures with U-Statistic Estimation: Theory, Simulation, and an Empirical Application to GDP per Capita in the Americas Vila, Roberto Saulo, Helton Methodology We introduce two families of inequality measures, $G_p$ and $H_q$, that converge to the classical Gini coefficient as $p,q\to\infty$. The tuning parameters $p>1$ and $q>0$ regulate the influence of disparities between observations. For each index we derive closed-form $U$-statistic plug-in estimators and establish strong consistency and asymptotic normality under mild moment conditions. A Monte Carlo study assesses finite-sample behavior across $(n,p,q)$, and an empirical illustration with GDP per capita in the Americas shows how the tuning parameters influence the measure of inequality. |
| title | Two Tunable Gini-Type Measures with U-Statistic Estimation: Theory, Simulation, and an Empirical Application to GDP per Capita in the Americas |
| topic | Methodology |
| url | https://arxiv.org/abs/2508.02965 |