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Visualizing Association Structure in Bivariate Copulas Using New Dependence Function

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Stochastic Models, Statistics and Their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 122))

Abstract

Measuring a strength of dependence of random variables is an important problem in statistical practice. We propose a new function valued measure of dependence of two random variables. It allows one to study and visualize explicit dependence structure, both in some theoretical models and empirically, without prior model assumptions. This provides a comprehensive view of association structure and makes possible much detailed inference than based on standard numeric measures of association. In this contribution, we focus on copula-based variant of the measure. We present theoretical properties of the new measure of dependence and discuss estimation of it. Some artificial and real data examples illustrate the behavior and practical utility of the measure and its estimator.

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Acknowledgements

Research was supported by the Grant N N201 608440 from the National Science Center, Poland. The author thanks Dr. Grzegorz Wyłupek for his help in preparing figures and the table of this article and for useful remarks. The author also thanks a referee for the careful reading of the manuscript and the useful comments.

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, ul. Kopernika 18, 51-617, Wrocław, Poland

    Teresa Ledwina

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  1. Teresa Ledwina
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Correspondence to Teresa Ledwina .

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Editors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Ansgar Steland

  2. Dept. of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wrocław, Poland

    Ewaryst Rafajłowicz

  3. Inst. of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Krzysztof Szajowski

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Ledwina, T. (2015). Visualizing Association Structure in Bivariate Copulas Using New Dependence Function. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_3

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