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A new rank correlation measure

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  • Claudio Borroni

Abstract

A new rank correlation measure β n is proposed, so as to develop a nonparametric test of independence for two variables. β n is shown to be the symmetrized version of a measure earlier proposed by Borroni and Zenga (Stat Methods Appl 16:289–308, 2007 ). More specifically, β n is built so that it can take the opposite sign, without changing its absolute value, when the ranking of one variable is reversed. Further, the meaning of the population equivalent of β n is discussed. It is pointed out that this latter association measure vanishes not only at independence but, more generally, at indifference, that is when the two variables do not show any “tendency” to positive or negative dependence. The null distribution of β n needs an independent study: hence, the finite null variance and a table of critical values are determined. Moreover, the asymptotic null distribution of β n is derived. Finally, the performance of the test based on β n is evaluated by simulation. β n is shown to be a good competitor of some classical tests for the same problem. Copyright Springer-Verlag 2013

Suggested Citation

  • Claudio Borroni, 2013. "A new rank correlation measure," Statistical Papers, Springer, vol. 54(2), pages 255-270, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:255-270
    DOI: 10.1007/s00362-011-0423-0
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    References listed on IDEAS

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    1. Claudio Borroni & Michele Zenga, 2007. "A test of concordance based on Gini’s mean difference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 289-308, November.
    2. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    3. Javad Behboodian & Ali Dolati & Manuel Úbeda-Flores, 2007. "A multivariate version of Gini's rank association coefficient," Statistical Papers, Springer, vol. 48(2), pages 295-304, April.
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    1. Claudio G. Borroni & D. Michele Cifarelli, 2017. "The influence function of Gini’s gamma," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 17-29, April.
    2. Claudio G. Borroni, 2019. "Mutual association measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 571-591, December.

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