IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v29y2010i3p247-275.html
   My bibliography  Save this article

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

Author

Listed:
  • Gordon Anderson
  • Ying Ge
  • Teng Wah Leo

Abstract

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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/07474930903451532
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

    More about this item

    Keywords

    Alienation; Convergence; Overlap index; Polarization;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:247-275. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.tandfonline.com/LECR20 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.