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Dependence Measuring from Conditional Variances

Author

Listed:
  • Kamnitui Noppadon

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Santiwipanont Tippawan

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Sumetkijakan Songkiat

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

Abstract

A conditional variance is an indicator of the level of independence between two random variables. We exploit this intuitive relationship and define a measure v which is almost a measure of mutual complete dependence. Unsurprisingly, the measure attains its minimum value for many pairs of non-independent ran- dom variables. Adjusting the measure so as to make it invariant under all Borel measurable injective trans- formations, we obtain a copula-based measure of dependence v* satisfying A. Rényi’s postulates. Finally, we observe that every nontrivial convex combination of v and v* is a measure of mutual complete dependence.

Suggested Citation

  • Kamnitui Noppadon & Santiwipanont Tippawan & Sumetkijakan Songkiat, 2015. "Dependence Measuring from Conditional Variances," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-15, July.
    • Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:15:n:7
    DOI: 10.1515/demo-2015-0007
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    References listed on IDEAS

    as
    1. Zheng, Yanting & Yang, Jingping & Huang, Jianhua Z., 2011. "Approximation of bivariate copulas by patched bivariate Fréchet copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 246-256, March.
    2. Trutschnig, Wolfgang, 2013. "On Cesáro convergence of iterates of the star product of copulas," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 357-365.
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