Article

Full entry | PDF   (0.2 MB)
Keywords:
copulas; distributions with given marginals; Frèchet–Hoeffding bounds; partial mutual independence
Summary:
We give a representation of the class of all $n$-dimensional copulas such that, for a fixed $m\in \mathbb N$, $2\le m < n$, all their $m$-dimensional margins are equal to the independence copula. Such an investigation originated from an open problem posed by Schweizer and Sklar.
References:
[1] V. Beneš, J. Štěpán, eds.: Distributions With Given Marginals and Moment Problems. Kluwer Academic Publishers, Dordrecht 1997. MR 1614650 | Zbl 0885.00054
[2] C. M. Cuadras, J. Fortiana, J. A. Rodriguez-Lallena, eds.: Distributions With Given Marginals and Statistical Modelling. Kluwer Academic Publishers, Dordrecht 2002. Papers from the meeting held in Barcelona 2000. MR 2058972 | Zbl 1054.62002
[3] G. Dall'Aglio, S. Kotz, G. Salinetti, eds.: Advances in Probability Distributions with Given Marginals. Mathematics and its Applications 67, Kluwer Academic Publishers Group, Dordrecht 1991. Beyond the Copulas, Papers from the Symposium on Distributions with Given Marginals held in Rome 1990. MR 1215942 | Zbl 0722.00031
[4] P. Deheuvels: Indépendance multivariée partielle et inégalités de Fréchet. In: Studies in Probability and Related Topics, Nagard, Rome 1983, pp. 145-155. MR 0778216 | Zbl 0557.60013
[5] F. Durante, E. P. Klement, J. J. Quesada-Molina: Bounds for trivariate copulas with given bivariate marginals. J. Inequal. Appl. 2008 (2008), 1-9. MR 2481572 | Zbl 1162.62047
[6] P. Jaworski, F. Durante, W. Härdle, T. Rychlik, eds.: Copula Theory and its Applications. Lecture Notes in Statistics - Proceedings 198, Springer, Berlin - Heidelberg 2010. Zbl 1194.62077
[7] H. Joe: Multivariate Models and Dependence Concepts. Monographs on Statistics and Applied Probability 73, Chapman & Hall, London 1997. MR 1462613 | Zbl 0990.62517
[8] R. B. Nelsen: An Introduction to Copulas. Second edition. Springer Series in Statistics, Springer, New York 2006. MR 2197664
[9] L. Rüschendorf, B. Schweizer, M. D. Taylor, eds.: Distributions with Fixed Marginals and Related Topics. Institute of Mathematical Statistics, Lecture Notes - Monograph Series 28, Hayward 1996. MR 1485518 | Zbl 0944.60012
[10] B. Schweizer, A. Sklar: Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics. North-Holland Publishing Co., New York 1983. Reprinted, Dover, Mineola 2005. MR 0790314 | Zbl 0546.60010
[11] K. F. Siburg, P. A. Stoimenov: Gluing copulas. Comm. Statist. Theory Methods 37 (2008), 19, 3124-3134. DOI 10.1080/03610920802074844 | MR 2467756
[12] A. Sklar: Fonctions de répartition à $n$ dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. MR 0125600

Partner of