A short note on multivariate dependence modeling

Bína, Vladislav, and Jiroušek, Radim. "A short note on multivariate dependence modeling." Kybernetika 49.3 (2013): 420-432. <http://eudml.org/doc/260742>.

@article{Bína2013,
abstract = {As said by Mareš and Mesiar, necessity of aggregation of complex real inputs appears almost in any field dealing with observed (measured) real quantities (see the citation below). For aggregation of probability distributions Sklar designed his copulas as early as in 1959. But surprisingly, since that time only a very few literature have appeared dealing with possibility to aggregate several different pairwise dependencies into one multivariate copula. In the present paper this problem is tackled using the well known Iterative Proportional Fitting Procedure. The proposed solution is not an exact mathematical solution of a marginal problem but just its approximation applicable in many practical situations like Monte Carlo sampling. This is why the authors deal not only with the consistent case, when the iterative procedure converges, but also with the inconsistent non-converging case. In the latter situation, the IPF procedure tends to cycle (when combining three pairwise dependencies the procedure creates three convergent subsequences), and thus the authors propose some heuristics yielding a ``solution'' of the problem even for inconsistent pairwise dependence relations.},
author = {Bína, Vladislav, Jiroušek, Radim},
journal = {Kybernetika},
keywords = {Frank copula; IPFP; entropy; Frank copula; iterative proportional fitting procedure; entropy},
language = {eng},
number = {3},
pages = {420-432},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A short note on multivariate dependence modeling},
url = {http://eudml.org/doc/260742},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Bína, Vladislav
AU - Jiroušek, Radim
TI - A short note on multivariate dependence modeling
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 3
SP - 420
EP - 432
AB - As said by Mareš and Mesiar, necessity of aggregation of complex real inputs appears almost in any field dealing with observed (measured) real quantities (see the citation below). For aggregation of probability distributions Sklar designed his copulas as early as in 1959. But surprisingly, since that time only a very few literature have appeared dealing with possibility to aggregate several different pairwise dependencies into one multivariate copula. In the present paper this problem is tackled using the well known Iterative Proportional Fitting Procedure. The proposed solution is not an exact mathematical solution of a marginal problem but just its approximation applicable in many practical situations like Monte Carlo sampling. This is why the authors deal not only with the consistent case, when the iterative procedure converges, but also with the inconsistent non-converging case. In the latter situation, the IPF procedure tends to cycle (when combining three pairwise dependencies the procedure creates three convergent subsequences), and thus the authors propose some heuristics yielding a ``solution'' of the problem even for inconsistent pairwise dependence relations.
LA - eng
KW - Frank copula; IPFP; entropy; Frank copula; iterative proportional fitting procedure; entropy
UR - http://eudml.org/doc/260742
ER -