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A new index to measure positive dependence in trivariate distributions

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  • García, Jesús E.
  • González-López, V.A.
  • Nelsen, R.B.

Abstract

We introduce a new index to detect dependence in trivariate distributions. The index is based on the maximization of the coefficients of directional dependence over the set of directions. We show how to calculate the index using the three pairwise Spearman’s rho coefficients and the three common 3-dimensional versions of Spearman’s rho. We obtain the asymptotic distributions of the empirical processes related to the estimators of the coefficients of directional dependence and also we derive the asymptotic distribution of our index. We display examples where the index identifies dependence undetected by the aforementioned 3-dimensional versions of Spearman’s rho. The value of the new index and the direction in which the maximal dependence occurs are easily computed and we illustrate with a simulation study and a real data set.

Suggested Citation

  • García, Jesús E. & González-López, V.A. & Nelsen, R.B., 2013. "A new index to measure positive dependence in trivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 481-495.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:481-495
    DOI: 10.1016/j.jmva.2012.11.007
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    References listed on IDEAS

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    7. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

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    4. César García Gómez & Ana Pérez & Mercedes Prieto-Alaiz, 2024. "Changes in the Dependence Structure of AROPE Components: Evidence from the Spanish Region," Hacienda Pública Española / Review of Public Economics, IEF, vol. 248(1), pages 21-51, March.

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