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Distributional Overlap: Simple, Multivariate, Parametric, and Nonparametric Tests for Alienation, Convergence, and General Distributional Difference Issues


  • Gordon Anderson
  • Ying Ge
  • Teng Wah Leo


This paper proposes a convenient measure of the degree of distributional overlap, both parametric and nonparametric, useful in measuring the degree of Polarization, Alienation, and Convergence. We show the measure is asymptotically normally distributed, making it amenable to inference in consequence. This Overlap measure can be used in the univariate and multivariate framework, and three examples are used to illustrate its use. The nonparametric Overlap Index has two sources of bias, the first being a positive bias induced by the unknown intersection point of the underlying distribution and the second being a negative bias induced by the expectation of cell probabilities being less than the conditional expected values. We show that the inconsistency problem generated by the first bias, prevalent within this class of Goodness of Fit measure, is limited by the number of intersection points of the underlying distributions. A Monte Carlo study was used to examine the biases, and it was found that the latter bias dominates the former. These biases can be diluted by increasing the number of partitions, but prevails asymptotically nonetheless.

Suggested Citation

  • Gordon Anderson & Ying Ge & Teng Wah Leo, 2010. "Distributional Overlap: Simple, Multivariate, Parametric, and Nonparametric Tests for Alienation, Convergence, and General Distributional Difference Issues," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 247-275.
  • Handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:247-275
    DOI: 10.1080/07474930903451532

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    References listed on IDEAS

    1. P. Brown & M. Melli & M. Cancian, "undated". "Physical Custody in Wisconsin Divorce Cases, 1980–1992," Institute for Research on Poverty Discussion Papers 1133-97, University of Wisconsin Institute for Research on Poverty.
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    Cited by:

    1. Iñaki Permanyer & Conchita D'Ambrosio, 2015. "Measuring Social Polarization with Ordinal and Categorical Data," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(3), pages 311-327, June.
    2. Anderson, Gordon & Linton, Oliver & Whang, Yoon-Jae, 2012. "Nonparametric estimation and inference about the overlap of two distributions," Journal of Econometrics, Elsevier, vol. 171(1), pages 1-23.
    3. Gordon Anderson & Teng Leo & Robert Muelhaupt, 2014. "Measuring Advances in Equality of Opportunity: The Changing Gender Gap in Educational Attainment in Canada in the Last Half Century," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 119(1), pages 73-99, October.
    4. Anderson, Gordon & Leo, Teng Wah, 2013. "An empirical examination of matching theories: The one child policy, partner choice and matching intensity in urban China," Journal of Comparative Economics, Elsevier, vol. 41(2), pages 468-489.

    More about this item


    Alienation; Convergence; Overlap index; Polarization;


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