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Dependence Modeling

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Dependence Measuring from Conditional Variances

Noppadon Kamnitui
  • Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Tippawan Santiwipanont
  • Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Songkiat Sumetkijakan
  • Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-07-22 | DOI: https://doi.org/10.1515/demo-2015-0007

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.

Keywords: conditional variances; measures of dependence; copulas; mutual complete dependence; shuffles of Min

MSC:: 60A10; 62H20

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About the article


Received: 2015-02-28

Accepted: 2015-07-02

Published Online: 2015-07-22


Citation Information: Dependence Modeling, Volume 3, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2015-0007.

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© 2015 N. Kamnitui et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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