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A true measure of dependence

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  • Li, Hui

Abstract

The strength of dependence between random variables is an important property that is useful in a lot of areas. Various measures have been proposed which detect mostly divergence from independence. However, a true measure of dependence should also be able to characterize complete dependence where one variable is a function of the other. Previous measures are mostly symmetric which are shown to be insufficient to capture complete dependence. A new type of nonsymmetric dependence measure is presented that can unambiguously identify both independence and complete dependence. The original Rényi’s axioms for symmetric measures are reviewed and modified for nonsymmetric measures.

Suggested Citation

  • Li, Hui, 2016. "A true measure of dependence," MPRA Paper 69735, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:69735
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    File URL: https://mpra.ub.uni-muenchen.de/69735/1/MPRA_paper_69735.pdf
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    References listed on IDEAS

    as
    1. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, September.
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    More about this item

    Keywords

    Nonsymmetric dependence measure; complete dependence; ∗ product on copula; Data Processing Inequality (DPI);
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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