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

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  • Kuan Xu

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.

Suggested Citation

  • Kuan Xu, 2007. "U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 567-577.
  • Handle: RePEc:taf:emetrv:v:26:y:2007:i:5:p:567-577
    DOI: 10.1080/07474930701512170
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    Cited by:

    1. Thomas Demuynck, 2012. "An (almost) unbiased estimator for the S-Gini index," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 109-126, March.
    2. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, Open Access Journal, vol. 4(3), pages 1-12, June.
    3. ANDREOLI Francesco & PELUSO Eugenio, 2017. "So close yet so unequal: Spatial inequality in American cities," LISER Working Paper Series 2017-11, LISER.
    4. 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.
    5. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    6. James E. 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.
    7. 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.
    8. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    9. repec:spr:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0140-3 is not listed on IDEAS
    10. Yong Tao & Xiangjun Wu & Changshuai Li, 2014. "Rawls' Fairness, Income Distribution and Alarming Level of Gini Coefficient," Papers 1409.3979, arXiv.org.

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