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Bounds on Multivariate Kendall’s Tau and Spearman’s Rho for Zero-Inflated Continuous Variables and their Application to Insurance

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  • Mhamed Mesfioui

    (Université du Québec à Trois-Rivières)

  • Julien Trufin

    (Université Libre de Bruxelles (ULB))

Abstract

In this note, we derive upper bounds on Kendall’s tau and Spearman’s rho for multivariate zero-inflated continuous variables often encountered in insurance. A lower bound for Spearman’s rho is also established in the bivariate case. These bounds are easy to compute and can be estimated from a data set of zero-inflated random vectors as illustrated in this note with a motor insurance portfolio.

Suggested Citation

  • Mhamed Mesfioui & Julien Trufin, 2022. "Bounds on Multivariate Kendall’s Tau and Spearman’s Rho for Zero-Inflated Continuous Variables and their Application to Insurance," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1051-1059, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09869-3
    DOI: 10.1007/s11009-021-09869-3
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    References listed on IDEAS

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    1. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    2. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2013. "On the estimation of Spearman’s rho and related tests of independence for possibly discontinuous multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 214-228.
    3. M. Taylor, 2007. "Multivariate measures of concordance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 789-806, December.
    4. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    5. Mesfioui, Mhamed & Quessy, Jean-François, 2010. "Concordance measures for multivariate non-continuous random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2398-2410, November.
    6. 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. Perrone, Elisa & van den Heuvel, Edwin R. & Zhan, Zhuozhao, 2023. "Kendall’s tau estimator for bivariate zero-inflated count data," Statistics & Probability Letters, Elsevier, vol. 199(C).

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