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.
@article{bwmeta1.element.doi-10_1515_demo-2015-0007,
author = {Noppadon Kamnitui and Tippawan Santiwipanont and Songkiat Sumetkijakan},
title = {Dependence Measuring from Conditional Variances},
journal = {Dependence Modeling},
volume = {3},
year = {2015},
zbl = {06534015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_demo-2015-0007}
}
Noppadon Kamnitui; Tippawan Santiwipanont; Songkiat Sumetkijakan. Dependence Measuring from Conditional Variances. Dependence Modeling, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_demo-2015-0007/
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