Published

2007-07-01

TEOREMAS CENTRAL DEL LÍMITE PARA EL S-GINI Y EL COEFICIENTE DE THEIL

CENTRAL LIMIT THEOREMS FOR S-GINI AND THEIL INEQUALITY COEFFICIENTS

Keywords:

índice S-Gini, índice de Theil, proceso húngaro, estimación kernel para la densidad (es)
S-Gini index, Theil index, Hungarian construction, Kernel density estimation (en)

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Authors

  • Pablo Martínez-Camblor Fundación Caubet-Cimera Illes Balears
Se usa el Proceso Húngaro (Komlós et al. 1975) para derivar la normalidad asintótica del S-Gini; Este método es muy interesante ya que puede ser usado para demostrar la normalidad asintótica de otros coeficientes usados para medir la desigualdad de ingresos como el de Theil. Se consiguen expresiones explícitas para la media y la varianza del S-Gini y del coeficiente de Theil. Finalmente, se realiza un estudio de simulación, en el que se compara el rendimiento de la aproximación asintótica propuesta y del método Bootstrap Suavizado.
The Hungarian Construction (Komlós et al. 1975) is used for getting a proof of asymptotic normality of S-Gini coefficient; this method is very interesting because it can be used to check asymptotic normality of other income inequality measures as Theil coefficient. Besides, explicit expressions of asymptotic means and variances are given for S-Gini and Theil estimators. Finally, to illustrate the performance of obtained results, we carry out a simulation study comparing the asymptotic and Smoothed Bootstrap approximations.

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Copyright (c) 2007 Revista Colombiana de Estadística

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