Abstract
In view of imprecise data in a variety of situations, we proceed to investigate dependence structure of random closed sets. Inspired by the modeling and quantifying of nonlinear dependence structures of random vectors, using copulas, we look at the extension of copula connection to the case of infinitely separable metric spaces with applications to the space of closed sets of a Hausdorff, locally compact, second countable space.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ayerbe Toledano, J.M., Dominguez Benavides, T., Lopez Acedo, T.: Measures of Noncompactness in Metric Fixed Point Theory. Birkhauser-Verlag, Basel (1997)
Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall/CRC (1997)
Matheron, G.: Random Sets and Integral Geometry. J. Wiley, Chichester (1975)
Molchanov, I.: Theory of Random Sets. Springer, Heidelberg (2005)
Nelsen, R.B.: An Introduction to Copulas. Springer, Heidelberg (2006)
Nguyen, H.T.: An Introduction to Random Sets. Chapman and Hall/CRC (2006)
Nguyen, H.T., Tran, H.: On a continuous lattice approach to modeling of coarse data in system analysis. Journal of Uncertain Systems 1(1), 62–73 (2007)
Nguyen, H.T., Nguyen, N.T.: A negative version of Choquet theorem for Polish spaces. East-West Journal of Mathematics 1, 61–71 (1998)
Resnick, S.I.: Heavy-Tail Phenomena, Probabilistic and Statistical Modeling. Springer, Heidelberg (2007)
Scarsini, M.: Copulae of probability measures on product spaces. J. Multivariate Anal. 31, 201–219 (1989)
Sklar, A.: Fonctions de repartition a n dimensions et leur marges. Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)
Strassen, V.: The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423–439 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nguyen, H.T. (2011). On Nonlinear Correlation of Random Elements. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-22833-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22832-2
Online ISBN: 978-3-642-22833-9
eBook Packages: EngineeringEngineering (R0)