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On the equivalence of conglomerability and disintegrability for unbounded random variables

Author

Listed:
  • Mark J. Schervish

    (Carnegie Mellon University)

  • Teddy Seidenfeld

    (Carnegie Mellon University
    Carnegie Mellon University)

  • Joseph B. Kadane

    (Carnegie Mellon University)

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.

Suggested Citation

  • Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 2014. "On the equivalence of conglomerability and disintegrability for unbounded random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 501-518, November.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:4:d:10.1007_s10260-014-0282-7
    DOI: 10.1007/s10260-014-0282-7
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    References listed on IDEAS

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    1. Patrizia Berti & Eugenio Regazzini & Pietro Rigo, 2001. "Strong previsions of random elements," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 11-28, January.
    2. Seidenfeld, Teddy & Schervish, Mark J. & Kadane, Joseph B., 2009. "Preference for equivalent random variables: A price for unbounded utilities," Journal of Mathematical Economics, Elsevier, vol. 45(5-6), pages 329-340, May.
    3. L. Crisma & P. Gigante, 2001. "A notion of coherent conditional prevision for arbitrary random quantities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 29-40, January.
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