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On rank correlation measures for non-continuous random variables

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  • Neslehová, Johanna

Abstract

For continuous random variables, many dependence concepts and measures of association can be expressed in terms of the corresponding copula only and are thus independent of the marginal distributions. This interrelationship generally fails as soon as there are discontinuities in the marginal distribution functions. In this paper, we consider an alternative transformation of an arbitrary random variable to a uniformly distributed one. Using this technique, the class of all possible copulas in the general case is investigated. In particular, we show that one of its members--the standard extension copula introduced by Schweizer and Sklar--captures the dependence structures in an analogous way the unique copula does in the continuous case. Furthermore, we consider measures of concordance between arbitrary random variables and obtain generalizations of Kendall's tau and Spearman's rho that correspond to the sample version of these quantities for empirical distributions.

Suggested Citation

  • Neslehová, Johanna, 2007. "On rank correlation measures for non-continuous random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 544-567, March.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:544-567
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    References listed on IDEAS

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    1. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    2. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
    3. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
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    Cited by:

    1. M. Shahe Emran & Francisco H. G. Ferreira & Yajing Jiang & Yan Sun, 2023. "Occupational dualism and intergenerational educational mobility in the rural economy: evidence from China and India," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(3), pages 743-773, September.
    2. Faugeras, Olivier P., 2015. "Maximal coupling of empirical copulas for discrete vectors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 179-186.
    3. Denuit, Michel & Mesfoui, Mhamed & Trufin, Julien, 2019. "Concordance-based predictive measures in regression models for discrete responses," LIDAM Discussion Papers ISBA 2019005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Denuit, Michel & Mesfioui, Mhamet & Trufin, Julien, 2016. "Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses," LIDAM Discussion Papers ISBA 2016046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Michel Denuit & Mhamed Mesfioui & Julien Trufin, 2019. "Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 491-509, June.

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