On the equivalence of conglomerability and disintegrability for unbounded random variables

Mark J. Schervish (), Teddy Seidenfeld () and Joseph B. Kadane ()
Additional contact information
Mark J. Schervish: Carnegie Mellon University
Teddy Seidenfeld: Carnegie Mellon University
Joseph B. Kadane: Carnegie Mellon University

Statistical Methods & Applications, 2014, vol. 23, issue 4, No 4, 518 pages

Abstract: Abstract We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglomerability). We give a sufficient condition to extend this result to collections of random variables that have finite expected value and whose conditional expectations are finite and have finite expected value.

Keywords: Finite additivity; Law of total probability; Daniell integral; Coherence; Primary 60A05; Secondary 28C05 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10260-014-0282-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stmapp:v:23:y:2014:i:4:d:10.1007_s10260-014-0282-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10260/PS2

DOI: 10.1007/s10260-014-0282-7

Access Statistics for this article

Statistical Methods & Applications is currently edited by Tommaso Proietti

More articles in Statistical Methods & Applications from Springer, Società Italiana di Statistica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().