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Estimating scale-invariant directed dependence of bivariate distributions

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  • Junker, Robert R.
  • Griessenberger, Florian
  • Trutschnig, Wolfgang

Abstract

Asymmetry of dependence is an inherent property of bivariate probability distributions. Being symmetric, commonly used dependence measures such as Pearson’s r or Spearman’s ρ mask asymmetry and implicitly assume that a random variable Y is equally dependent on a random variable X as vice versa. A copula-based, hence scale-invariant dependence measure called ζ1 overcoming the just mentioned problem was introduced in 2011. ζ1 attains values in [0,1], it is 0 if, and only if X and Y are independent, and 1 if, and only if Y is a measurable function of X. Working with so-called empirical checkerboard copulas allows to construct an estimator ζ1n for ζ1 which is strongly consistent in full generality, i.e., without any smoothness assumptions on the underlying copula. The R-package qad (short for quantification of asymmetric dependence) containing the estimator ζ1n is used both, to perform a simulation study illustrating the small sample performance of the estimator as well as to estimate the directed dependence between some global climate variables as well as between world development indicators.

Suggested Citation

  • Junker, Robert R. & Griessenberger, Florian & Trutschnig, Wolfgang, 2021. "Estimating scale-invariant directed dependence of bivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    • Handle: RePEc:eee:csdana:v:153:y:2021:i:c:s0167947320301493
    DOI: 10.1016/j.csda.2020.107058
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    References listed on IDEAS

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    3. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2024. "On comprehensive families of copulas involving the three basic copulas and transformations thereof," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-36.
    4. Fuchs Sebastian & Trutschnig Wolfgang, 2020. "On quantile based co-risk measures and their estimation," Dependence Modeling, De Gruyter, vol. 8(1), pages 396-416, January.
    5. Ben Jabeur, Sami & Boubaker, Sabri & Carmona, Pedro & Stef, Nicolae, 2025. "How do environmental concerns and global economic conditions affect energy prices?," Energy Policy, Elsevier, vol. 204(C).
    6. Wei, Zheng & Kim, Daeyoung, 2021. "Measure of asymmetric association for ordinal contingency tables via the bilinear extension copula," Statistics & Probability Letters, Elsevier, vol. 178(C).
    7. Ansari Jonathan & Rockel Marcus, 2024. "Dependence properties of bivariate copula families," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-36.
    8. JD Opdyke, 2025. "Beyond Correlation: Positive Definite Dependence Measures for Robust Inference, Flexible Scenarios, and Causal Modeling for Financial Portfolios," Papers 2504.15268, arXiv.org, revised Jan 2026.
    9. Arriaza, Antonio & Navarro, Jorge & Ortega-Jiménez, Patricia, 2024. "Risk times in mission-oriented systems," LIDAM Discussion Papers ISBA 2024017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Griessenberger Florian & Trutschnig Wolfgang, 2022. "Maximal asymmetry of bivariate copulas and consequences to measures of dependence," Dependence Modeling, De Gruyter, vol. 10(1), pages 245-269, January.
    11. Fuchs Sebastian & Trutschnig Wolfgang, 2020. "On quantile based co-risk measures and their estimation," Dependence Modeling, De Gruyter, vol. 8(1), pages 396-416, January.

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