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Measuring association and dependence between random vectors

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  • Grothe, Oliver
  • Schnieders, Julius
  • Segers, Johan

Abstract

Measures of association are suggested between two random vectors. The measures are copula-based and therefore invariant with respect to the univariate marginal distributions. The measures are able to capture positive as well as negative association. In case the random vectors are just random variables, the measures reduce to Kendall’s tau or Spearman’s rho. Nonparametric estimators, based on ranks, for the measures are derived. Their large-sample asymptotics are derived and their small-sample behavior is investigated by simulation. The measures are applied to characterize strength and direction of association of northern and southern European bond markets during the recent Euro crisis as well as association of stock markets with bond markets.

Suggested Citation

  • Grothe, Oliver & Schnieders, Julius & Segers, Johan, 2014. "Measuring association and dependence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 96-110.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:96-110
    DOI: 10.1016/j.jmva.2013.08.019
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    References listed on IDEAS

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    Cited by:

    1. Liebscher, Eckhard, 2021. "Kendall regression coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Yanqin Fan & Marc Henry, 2020. "Vector copulas," Papers 2009.06558, arXiv.org, revised Apr 2021.
    3. Fuchs, Sebastian & Di Lascio, F. Marta L. & Durante, Fabrizio, 2021. "Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    4. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Fan, Yanqin & Henry, Marc, 2023. "Vector copulas," Journal of Econometrics, Elsevier, vol. 234(1), pages 128-150.
    6. Liebscher Eckhard, 2014. "Copula-based dependence measures," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-16, October.
    7. Lingyue Zhang & Dawei Lu & Xiaoguang Wang, 2020. "Measuring and testing interdependence among random vectors based on Spearman’s $$\rho $$ ρ and Kendall’s $$\tau $$ τ," Computational Statistics, Springer, vol. 35(4), pages 1685-1713, December.
    8. Betken, Annika & Dehling, Herold & Nüßgen, Ines & Schnurr, Alexander, 2021. "Ordinal pattern dependence as a multivariate dependence measure," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    9. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    10. Liebscher Eckhard, 2017. "Copula-Based Dependence Measures For Piecewise Monotonicity," Dependence Modeling, De Gruyter, vol. 5(1), pages 198-220, August.

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