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Conditional expectations and idempotent copulæ. (English) Zbl 1142.62355
Cuadras, Carles M. (ed.) et al., Distributions with given marginals and statistical modelling. Papers presented at the meeting, Barcelona, Spain, July 17–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0914-3/hbk). 223-228 (2002).
Summary: 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 W. F. Darsow, B. Nguyen and E. T. Olsen [Ill. J. Math. 36, No. 4, 600–642 (1992; Zbl 0770.60019)].
For the entire collection see [Zbl 1054.62002].

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
62A01 Foundations and philosophical topics in statistics