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An Exhaustive Coefficient Of Rank Correlation

Author

Listed:
  • Agostino Tarsitano

    ()

  • Rosetta Lombardo

    () (Dipartimento di Economia e Statistica, Università della Calabria)

Abstract

Rank association is a fundamental tool for expressing dependence in cases in which data are arranged in order. Measures of rank correlation have been accumulated in several contexts for more than a century and we were able to cite more than thirty of these coefficients, from simple ones to relatively complicated definitions invoking one or more systems of weights. However, only a few of these can actually be considered to be admissible substitutes for Pearson’s correlation. The main drawback with the vast majority of coefficients is their “resistance-tochange” which appears to be of limited value for the purposes of rank comparisons that are intrinsically robust. In this article, a new nonparametric correlation coefficient is defined that is based on the principle of maximization of a ratio of two ranks. In comparing it with existing rank correlations, it was found to have extremely high sensitivity to permutation patterns. We have illustrated the potential improvement that our index can provide in economic contexts by comparing published results with those obtained through the use of this new index. The success that we have had suggests that our index may have important applications wherever the discriminatory power of the rank correlation coefficient should be particularly strong.

Suggested Citation

  • Agostino Tarsitano & Rosetta Lombardo, 2011. "An Exhaustive Coefficient Of Rank Correlation," Working Papers 201111, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
  • Handle: RePEc:clb:wpaper:201111
    as

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    File URL: http://www.ecostat.unical.it/RePEc/WorkingPapers/WP11_2011.pdf
    File Function: First version, 2011-10
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    References listed on IDEAS

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    1. Michael Gapen & Dale Gray & Cheng Hoon Lim & Yingbin Xiao, 2008. "Measuring and Analyzing Sovereign Risk with Contingent Claims," IMF Staff Papers, Palgrave Macmillan, vol. 55(1), pages 109-148, April.
    2. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    3. Shieh, Grace S., 1998. "A weighted Kendall's tau statistic," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 17-24, July.
    4. Korhonen, Pekka & Siljamaki, Aapo, 1998. "Ordinal principal component analysis theory and an application," Computational Statistics & Data Analysis, Elsevier, vol. 26(4), pages 411-424, February.
    5. William Horrace & Joseph Marchand & Timothy Smeeding, 2008. "Ranking inequality: Applications of multivariate subset selection," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 5-32, March.
    6. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    7. repec:spr:spbrec:978-81-322-1130-3 is not listed on IDEAS
    8. Robert J. Hill, 1999. "Comparing Price Levels across Countries Using Minimum-Spanning Trees," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 135-142, February.
    9. Maurizio Brizzi, 1992. "Misure di variabilità, concentrazione e dissomiglianza come sintesi di rapporti," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
    10. Vito Peragine, 2004. "Ranking Income Distributions According to Equality of Opportunity," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(1), pages 11-30, April.
    11. Roll, Richard, 1978. "Ambiguity when Performance is Measured by the Securities Market Line," Journal of Finance, American Finance Association, vol. 33(4), pages 1051-1069, September.
    12. Daniele Checchi, 1997. "Education and Intergenerational Mobility in Occupations," Vierteljahrshefte zur Wirtschaftsforschung / Quarterly Journal of Economic Research, DIW Berlin, German Institute for Economic Research, vol. 66(1), pages 136-144.
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    More about this item

    Keywords

    Ordinal data; Nonparametric agreement; Economic applications;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines

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