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U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures

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  • Kuan Xu
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Abstract

U-statistics form a general class of statistics that have certain important features in common. This class arises as a generalization of the sample mean and the sample variance, and typically members of the class are asymptotically normal with good consistency properties. The class encompasses some widely used income inequality and poverty measures, in particular the variance, the Gini index, the poverty rate, the average poverty gap ratios, the Foster-Greer-Thorbecke index, and the Sen index and its modified form. This paper illustrates how these measures come together within the class of U-statistics, and thereby why U-statistics are useful in econometrics.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 26 (2007)
Issue (Month): 5 ()
Pages: 567-577

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Handle: RePEc:taf:emetrv:v:26:y:2007:i:5:p:567-577

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Keywords: Asymptotic theory; Inequality; Measures; Poverty; U-statistics;

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Cited by:
  1. T. Demuynck, 2009. "An (almost) unbiased estimator for the S-Gini index," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/569, Ghent University, Faculty of Economics and Business Administration.
  2. Russell Davidson, 2007. "Reliable Inference For The Gini Index," Working Papers halshs-00353856, HAL.
  3. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
  4. Judith A. Clarke & Ahmed A. Hoque, 2014. "On Variance Estimation for a Gini Coefficient Estimator Obtained from Complex Survey Data," Econometrics Working Papers 1401, Department of Economics, University of Victoria.
  5. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," Journal of Economic Inequality, Springer, vol. 8(4), pages 491-524, December.
  6. Yoonseok Lee & Donggyun Shin, 2013. "Measuring Social Unrest Based on Income Distribution," Center for Policy Research Working Papers 160, Center for Policy Research, Maxwell School, Syracuse University.

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