Abstract
One of the efficient ways to describe the dependence between random variables is by describing the corresponding copula. For continuous distributions, the copula is uniquely determined by the corresponding distribution. However, when the distributions are not continuous, the copula is no longer unique, what is unique is a subcopula, a function C(u, v) that has values only for some pairs (u, v). From the purely mathematical viewpoint, it may seem like subcopulas are not needed, since every subcopula can be extended to a copula. In this paper, we prove, however, that from the algorithmic viewpoint, it is, in general, not possible to always generate a copula. Thus, from the algorithmic viewpoint, subcopulas are needed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bishop, E., Bridges, D.: Constructive Analysis. Springer Verlag, Heidelberg (1985)
Fernández-Sánchez, J., Úbeda-Flores, M.: Proving Sklar’s theorem via Zorn’s lemma. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 26(1), 81–85 (2018)
Jaworski, P., Durante, F., Härdle, W.K., Rychlik, T. (eds.): Copula Theory and Its Applications. Springer, Heidelberg (2010)
Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1997)
Kreinovich, V., Pownuk, A., Kosheleva, O.: Combining interval and probabilistic uncertainty: what is computable? In: Pardalos, P., Zhigljavsky, A., Zilinskas, J. (eds.) Advances in Stochastic and Deterministic Global Optimization, pp. 13–32. Springer, Cham (2016)
Mai, J.-F., Scherer, M.: Simulating Copulas: Stochastic Models, Sampling Algorithms, and Applications. World Scientific, Singapore (2017)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton (2015)
Nelsen, R.B.: An Introduction to Copulas. Springer, Heidelberg (2007)
Okhrin, O., Okhrin, Y., Schmidt, W.: On the structure and estimation of hierarchical Archimedean copulas. J. Econ. 173, 189–204 (2013)
Rabinovich, S.G.: Measurement Errors and Uncertainty: Theory and Practice. Springer, Berlin (2005)
Ruppert, M.: Contributions to Static and Time-varying Copula-based Modeling of Multivariate Association. EUL Verlag, Koeln (2012)
Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton (2011)
Wei, Z., Wang, T., Nguyen, P.A.: Multivariate dependence concepts through copulas. Int. J. Approx. Reason. 65(1), 24–33 (2015)
Wei, Z., Wang, T., Panichkitkosolkul, W.: Dependence and association concepts through copulas. In: Huynh, V.-N., Kreinovich, V., Sriboonchitta, S. (eds.) Modeling Dependence in Econometrics, pp. 113–126. Springer, Cham (2014)
Weihrauch, K.: Computable Analysis. Springer, Berlin (2000)
Zhang, Y., Beer, M., Quek, S.T.: Long-term performance assessment and design of offshore structures. Comput. Struct. 154, 101–115 (2015)
Zhu, X., Wang, T., Choy, S.T.B., Autchariyapanitkul, K.: Measures of mutually complete dependence for discrete random vectors. In: Kreinovich, V., Sriboonchitta, S., Chakpitak, N. (eds.) Predictive Econometrics and Big Data, pp. 303–317. Springer, Cham (2018)
Acknowledgments
This work was supported in part by the US National Science Foundation via grant HRD-1242122 (Cyber-ShARE Center of Excellence).
The authors are thankful to Professor Hung T. Nguyen for valuable discussions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Nguyen, T.N., Kosheleva, O., Kreinovich, V., Nguyen, H.P. (2019). Algorithmic Need for Subcopulas. In: Kreinovich, V., Sriboonchitta, S. (eds) Structural Changes and their Econometric Modeling. TES 2019. Studies in Computational Intelligence, vol 808. Springer, Cham. https://doi.org/10.1007/978-3-030-04263-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-04263-9_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-04262-2
Online ISBN: 978-3-030-04263-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)