# A short note on multivariate dependence modeling

Vladislav Bína; Radim Jiroušek

Kybernetika (2013)

- Volume: 49, Issue: 3, page 420-432
- ISSN: 0023-5954

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topBína, 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 -

## References

top- Aas, K., Czado, C., Frigessi, A., Bakken, H., 10.1016/j.insmatheco.2007.02.001, Insurance Math. Econom. 44, 2 (2009), 182-198. MR2517884DOI10.1016/j.insmatheco.2007.02.001
- Asci, C., Piccioni, M., A note on the IPF algorithm when the marginal problem is unsolvable., Kybernetika 39 (2003), 6, 731-737. Zbl1245.62070MR2035647
- Csiszár, I., 10.1214/aop/1176996454, Ann. Probab. 3 (1975), 146-158. Zbl0318.60013MR0365798DOI10.1214/aop/1176996454
- Deming, W. E., Stephan, F. F., 10.1214/aoms/1177731829, Ann. Math. Statist. 11 (1940), 427-444. MR0003527DOI10.1214/aoms/1177731829
- Hennessy, D. A., Lapan, H. E., 10.1111/1467-9965.00136, Math. Finance 12 (2002), 2, 143-154. MR1891733DOI10.1111/1467-9965.00136
- Jiroušek, R., Solution of the marginal problem and decomposable distributions., Kybernetika 27, 5 (1991), 403-412. Zbl0752.60009MR1132602
- Kratochvíl, V., Characteristic properties of equivalent structures in compositional models. Zbl1214.68400
- Li, D. X., 10.3905/jfi.2000.319253, J. Fixed Income 9 (2000), 4, 43-54. DOI10.3905/jfi.2000.319253
- Mareš, M., Mesiar, R., Aggregation of complex quantities., In: Proceedings of AGOP'2005. International Summer School on Aggregation Operators and Their Applications (R. Mesiar, G. Pasi, and M. Faré, eds.), Universitá della Svizzeria Italiana, Lugano 2005, pp. 85-88.
- Rüschendorf, L., 10.1214/aos/1176324703, Ann. Statist. 23 (1995), 4, 1160-1174. Zbl0851.62038MR1353500DOI10.1214/aos/1176324703
- Sklar, A., Fonctions de répartition à n dimensions et leurs marges., Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231 . MR0125600
- Schirmacher, D., Schirmacher, E., Multivariate Dependence Modeling Using Pair-copulas., Technical Report, Society of Acturaries, Enterprise Risk Management Symposium, Chicago 2008.
- Vomlel, J., 10.3166/jancl.14.367-386, J. Appl. Non-Classical Logics 14 (2004), 3, 367-386. Zbl1185.68699DOI10.3166/jancl.14.367-386
- Weiss, G. N. F., Copula parameter estimation: numerical considerations and implications for risk management., J. Risk 13 (2010), 1, 17-53.

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