¹Ferdowsi University of Mashhad, Faculty of science, Department of Statistics, Mashhad, Iran. PhD. Email: sh.mirzaei@stu.um.ac.ir
²Ferdowsi University of Mashhad, Faculty of science, Department of Statistics, Mashhad, Iran. PhD. Email: grmohtashami@um.ac.ir
³Ferdowsi University of Mashhad, Faculty of science, Department of Statistics, Mashhad, Iran. PhD. Email: m-amini@um.ac.ir

In this paper, we consider two well-known methods for analysis of the Gini index, which are U-statistics and linearization for some income distributions. In addition, we evaluate two different methods for some properties of their proposed estimators. Also, we compare two methods with resampling techniques in approximating some properties of the Gini index. A simulation study shows that the linearization method performs well compared to the Gini estimator based on U-statistics. A brief study on real data supports our findings.

Key words: Gini coefficient, Income distribution, Linearization method, Resampling techniques, U-statistics.

En este artículo consideramos dos métodos ampliamente conocidos para en análisis del índice Gini, los cuales son U-statistics y linealización. Adicionalmente, evaluamos los dos métodos diferentes con base en las propiedades de los estimadores propuestos sobre distribuciones de la renta. También comparamos los métodos con técnicas de remuestreo aproximando algunas propiedades del índice Gini. Un estudio de simulación muestra que el método de linealización se comporta "bien" comparado con el método basado en U-statistics. Un corto estudio de datos reales confirma nuestro resultado.

Palabras clave: índice Gini, distribuciones de la renta, método de linealización, técnicas de remuestreo, U-statistics.

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References

1. Arcagni, A. & Porro, F. (2014), 'The graphical reprensentation of inequality', Revista Colombiana de Estadística 37, 419-436.         [ Links ]

2. Barrett, G. F. & Donald, S. G. (2009), 'Statistical inference with generalized Gini indices of inequality, poverty, and welfare', Journal of Business & Economic Statistics 27, 1-17.         [ Links ]

3. Berger, Y. G. (2008), 'A note on the asymptotic equivalence of jackknife and linearization variance estimation for the Gini coefficient', Journal of Statist 24(1), 541-555.         [ Links ]

4. Bishop, J. A., Formby, J. P. & Zheng, B. (1997), 'Statistical inference and the Sen index of poverty', International Economic Review 150, 381-387.         [ Links ]

5. Davidson, R. (2009), 'Reliable inference for the Gini index', Journal of econometrics 150(1), 30-40.         [ Links ]

6. Gastwirth, J. L. (1971), 'A general definition of the Lorenz curve', Econometrica 39, 1037-1039.         [ Links ]

7. Giles, D. E. (2004), 'Calculating a standard error for the Gini coefficient: some further results', Oxford Bulletin of Economics and Statistics 66(1), 425-433.         [ Links ]

8. Giles, D. E. (2006), 'A cautionary note on estimating the standard error of the Gini index of inequality: comment', Oxford Bulletin of Economics and Statistics 68(1), 395-396.         [ Links ]

9. Hoeffding, W. (1948), 'A class of statistics with asymptotically normal distribution', The Annals of Mathematical Statistics 19(1), 293-325.         [ Links ]

10. Knight, K. (1999), Mathematical Statistics, John Wiley & Sons, New York.         [ Links ]

11. Langel, M. & Tillè, Y. (2013), 'Variance estimation of the Gini index: revisiting a result several times published', Journal of the Royal Statistical Society-Series A 176, 521-540.         [ Links ]

12. Lerman, R. I. & Yitzhaki, S. (1984), 'A note on the calculation and interpretation of the Gini index', Economics Letters de Estadistica 15, 363-368.         [ Links ]

13. Mills, J. A. & Zandvakili, S. (1997), 'Statistical inference via bootstrapping for measures of inequality', Journal of Applied econometrics 12, 133-150.         [ Links ]

14. Modarres, R. & Gastwirth, J. L. (2006), 'A cautionary note on estimating the standard error of the Gini index of inequality', Oxford Bulletin of Economics and Statistics 68(1), 391-393.         [ Links ]

15. Ogwang, T. (2000), 'A convenient method of computing the Gini index and its standard error', Oxford Bulletin of Economics and Statistics 47, 123-129.         [ Links ]

16. Serfling, R. J. (2009), Approximation theorems of mathematical statistics, John Wiley & Sons, New York.         [ Links ]

17. Shalit, H. (1985), 'Calculating the Gini index of inequality for individual data', Oxford Bulletin of Economics and Statistics 47, 185-189.         [ Links ]

18. Wolfe, D. & Randles, R. (1973), Introduction to the Theory of Nonparametric Statistics, Wiley, New York.         [ Links ]

19. Xu, K. (2003), 'How has the literature on Gini's index evolved in the past 80 years?', Dalhousie University, Economics Working Paper.         [ Links ]

20. Xu, K. (2007), 'U-statistics and their asymptotic results for some inequality and poverty measures', Econometric Reviews 26, 567-577.         [ Links ]

21. Yitzhaki, S. (1991), 'Calculating jackknife variance estimators for parameters of the Gini method', Journal of Business & Economic Statistics 9, 235-239.         [ Links ]

22. Yitzhaki, S. (1998), 'More than a dozen alternative ways of spelling Gini', Research on economic inequality 8, 13-30.         [ Links ]

23. Yitzhaki, S. & Schechtman, E. (2013), The Gini Methodology: A primer on a Statistical Methodology, Springer, New York.         [ Links ]

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