Dependence Measuring from Conditional Variances

Kamnitui Noppadon, Santiwipanont Tippawan and Sumetkijakan Songkiat
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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

Dependence Modeling, 2015, vol. 3, issue 1, 15

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; 60A10; 62H20; conditional variances; measures of dependence; copulas; mutual complete dependence; shuffles of Min; 60A10; 62H20 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:3:y:2015:i:1:p:15:n:7

DOI: 10.1515/demo-2015-0007

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