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Nonparametric estimation of a polarization measure

  • Gordon Anderson


  • Oliver Linton


  • Yoon-Jae Whang


This paper develops methodology for nonparametric estimation of a polarization measure due to Anderson (2004) and Anderson, Ge, and Leo (2006) based on kernel estimation techniques. We give the asymptotic distribution theory of our estimator, which in some cases is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we095130.

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Date of creation: Jun 2009
Date of revision:
Handle: RePEc:cte:werepe:we095130
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  1. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  2. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2003. "Polarization: Concepts, Measurement, Estimation," Working Papers 46, Barcelona Graduate School of Economics.
  3. Joan-Maria Esteban & Debraj Ray, 1991. "On the Measurement of Polarization," Boston University - Institute for Economic Development 18, Boston University, Institute for Economic Development.
  4. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
  6. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
  7. Holmström, Lasse & Klemelä, Jussi, 1992. "Asymptotic bounds for the expected L1 error of a multivariate kernel density estimator," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 245-266, August.
  8. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  9. Clemons, Traci E. & Jr., Edwin L. Bradley, 2000. "A nonparametric measure of the overlapping coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 34(1), pages 51-61, July.
  10. Schmid, Friedrich & Schmidt, Axel, 2006. "Nonparametric estimation of the coefficient of overlapping--theory and empirical application," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1583-1596, March.
  11. Knight, J. & Shi, L. & Renwei, Z., 1999. "A Spatial Analysis of Wages and Incomes in Urban China: Divergent Means, Convergent Inequality," Economics Series Working Papers 99209, University of Oxford, Department of Economics.
  12. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
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