Abstract
Abstract A connection between conditional expectations and idempotent copulas is established. It is proved that there exists a one-to-one correspondence between conditional expectations and copulas that are idempotent with respect to the binary operation introduced by Darsow, Nguyen and Olsen.
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
Preview
Unable to display preview. Download preview PDF.
References
R.R. Bahadur (1955), Measurable subspaces and subalgebras, Proc. Amer. Math. Soc. 6, 565–570.
W.F. Darsow, B. Nguyen, E.T. Olsen (1992), Copulas and Markov processes, Illinois Journal of Math.36, 600–642.
R.B. Nelsen (1999), An introduction to copulas, Lecture Notes in Statistics 139, Springer, New York.
E.T. Olsen, W.F. Darsow, B. Nguyen (1996), Copulas and Markov operators, In: L. Rüschendorf, B. Schweizer, M. D. Taylor, (Eds.), Distributions with fixed marginals and related topics, Institute of Mathematical Statistics (Lecture Notes — Monograph Series Volume 28) Hayward CA, pp. 244–259.
J. Pfanzagl (1967), Characterizations of conditional expectations, Ann. Math. Statist. 28, 415–421.
B. Schweizer, A. Sklar (1983), Probabilistic metric spaces, North—Holland, New York.
B. Schweizer (1991), Thirty years of copulas, In: G. Dall’Aglio, S. Katz, G. Salinetti, (Eds.), Probability distributions with given marginals, Kluwer, Dordrecht, pp. 13–50.
C. Sempi (1986), Le speranze condizionate e loro caratterizzazioni, Quaderni del Dipartimento di Matematica, Università di Lecce, Q-4.
Z. Šidák (1957), On relations between strict—sense and wide—sense conditional expectations, Theory Probab. Appl. 2, 267–272.
A. Sklar (1959), Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8, 229–231.
A. Sklar (1973), Random variables, joint distribution functions and copulas, Kybernetika 9, 449–460.
A. Sklar (1996), Random variables, distribution functions, and copulas — A personal look backward and forward, In: L. Rüschendorf, B. Schweizer, M.D. Taylor, (Eds.), Distributions with fixed marginals and related topics, Institute of Mathematical Statistics (Lecture Notes — Monograph Series Volume 28) Hayward CA, pp. 1–14.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Sempi, C. (2002). Conditional Expectations and Idempotent Copulæ. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_23
Download citation
DOI: https://doi.org/10.1007/978-94-017-0061-0_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6136-2
Online ISBN: 978-94-017-0061-0
eBook Packages: Springer Book Archive