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

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  • Kuan Xu

    (Department of Economics, Dalhousie University)

Abstract

U-statistics form a general class of statistics which 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, average poverty gap ratios, the Foster-Greer-Thorbecke index, 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, 2006. "U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures," Working Papers daleconwp2007-06, Dalhousie University, Department of Economics.
    • Handle: RePEc:dal:wpaper:daleconwp2007-06
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    References listed on IDEAS

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    Cited by:

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    2. Francesco Andreoli & Eugenio Peluso, 2016. "So close yet so unequal: Reconsidering spatial inequality in U.S. cities," Working Papers 21/2016, University of Verona, Department of Economics.
    3. Francesco Andreoli & Eugenio Peluso, 2021. "Inference for the neighbourhood inequality index," Spatial Economic Analysis, Taylor & Francis Journals, vol. 16(3), pages 313-332, July.
    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. 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.
    6. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    7. Yang Wei & Zhouping Li & Yunqiu Dai, 2022. "Unified smoothed jackknife empirical likelihood tests for comparing income inequality indices," Statistical Papers, Springer, vol. 63(5), pages 1415-1475, October.
    8. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    9. ANDREOLI Francesco & PELUSO Eugenio, 2017. "So close yet so unequal: Spatial inequality in American cities," LISER Working Paper Series 2017-11, Luxembourg Institute of Socio-Economic Research (LISER).
    10. Philippe De Vreyer & Sylvie Lambert, 2021. "Inequality, Poverty, and the Intra-Household Allocation of Consumption in Senegal," The World Bank Economic Review, World Bank, vol. 35(2), pages 414-435.
    11. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2013. "Nash‐Bargained Consumption Decisions: A Revealed Preference Analysis," Economic Journal, Royal Economic Society, vol. 123, pages 195-235, March.
    12. Yoonseok Lee & Donggyun Shin, 2016. "Measuring Social Tension from Income Class Segregation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 457-471, July.
    13. Yong Tao & Xiangjun Wu & Changshuai Li, 2014. "Rawls' Fairness, Income Distribution and Alarming Level of Gini Coefficient," Papers 1409.3979, arXiv.org.
    14. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.
    15. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 43(4), pages 1122-1148, November.
    16. Ilaria Benedetti & Federico Crescenzi & Tiziana Laureti, 2020. "Measuring Uncertainty for Poverty Indicators at Regional Level: The Case of Mediterranean Countries," Sustainability, MDPI, vol. 12(19), pages 1-19, October.
    17. 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.
    18. 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.
    19. Sylvie Lambert & Philippe De Vreyer, 2017. "By ignoring intra-household inequality do we underestimate the extent of poverty?," Working Papers DT/2017/05, DIAL (Développement, Institutions et Mondialisation).
    20. Shyamal K. De & Bhargab Chattopadhyay, 2017. "Minimum Risk Point Estimation of Gini Index," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 247-277, November.

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