Dependence Measuring from Conditional Variances

Noppadon Kamnitui; Tippawan Santiwipanont; Songkiat Sumetkijakan

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 98-112, electronic only
  • ISSN: 2300-2298

Abstract

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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.

How to cite

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Noppadon Kamnitui, Tippawan Santiwipanont, and Songkiat Sumetkijakan. "Dependence Measuring from Conditional Variances." Dependence Modeling 3.1 (2015): 98-112, electronic only. <http://eudml.org/doc/271033>.

@article{NoppadonKamnitui2015,
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.},
author = {Noppadon Kamnitui, Tippawan Santiwipanont, Songkiat Sumetkijakan},
journal = {Dependence Modeling},
keywords = {conditional variances; measures of dependence; copulas; mutual complete dependence; shuffles of Min; shuffles of Min},
language = {eng},
number = {1},
pages = {98-112, electronic only},
title = {Dependence Measuring from Conditional Variances},
url = {http://eudml.org/doc/271033},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Noppadon Kamnitui
AU - Tippawan Santiwipanont
AU - Songkiat Sumetkijakan
TI - Dependence Measuring from Conditional Variances
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 98
EP - 112, electronic only
AB - 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.
LA - eng
KW - conditional variances; measures of dependence; copulas; mutual complete dependence; shuffles of Min; shuffles of Min
UR - http://eudml.org/doc/271033
ER -

References

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