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An Exhaustive Coefficient Of Rank Correlation

  • Agostino Tarsitano


  • Rosetta Lombardo


    (Dipartimento di Economia e Statistica, Università della Calabria)

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    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.

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    Paper provided by Università della Calabria, Dipartimento di Economia, Statistica e Finanza (Ex Dipartimento di Economia e Statistica) in its series Working Papers with number 201111.

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    Length: 29 pages
    Date of creation: Oct 2011
    Date of revision:
    Handle: RePEc:clb:wpaper:201111
    Contact details of provider: Postal: Università della Calabria, Dipartimento di Economia, Statistica e Finanza, Ponte Pietro Bucci, Cubo 0/C, I-87036 Arcavacata di Rende, CS, Italy
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    1. 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.
    2. repec:bot:quadip:60 is not listed on IDEAS
    3. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods and Applications, Springer, vol. 19(4), pages 497-515, November.
    4. 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.
    5. Vito Peragine, 2004. "Ranking Income Distributions According to Equality of Opportunity," Journal of Economic Inequality, Springer, vol. 2(1), pages 11-30, April.
    6. William C. Horrace & Joseph T. Marchand & Timothy M. Smeeding, 2005. "Ranking Inequality: Applications of Multivariate Subset Selection," Center for Policy Research Working Papers 70, Center for Policy Research, Maxwell School, Syracuse University.
    7. Maurizio Brizzi, 1992. "Misure di variabilità, concentrazione e dissomiglianza come sintesi di rapporti," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
    8. 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.
    9. Roll, Richard, 1978. "Ambiguity when Performance is Measured by the Securities Market Line," Journal of Finance, American Finance Association, vol. 33(4), pages 1051-69, September.
    10. 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.
    11. 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.
    12. Shieh, Grace S., 1998. "A weighted Kendall's tau statistic," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 17-24, July.
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