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A simple proof of the almost sure discreteness of a class of random measures

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  • James, Lancelot F.

Abstract

A simple proof of the almost sure discreteness of a class of random measures which includes completely random measures is presented. The method of proof shows how one may extend the specific argument of Berk and Savage (Berk and Savage Contributions to Statistics, Jaroslev Hájek Memorial Volume, Reidel, Dordrecht, Boston, Massachusetts, London, 25 (1979)) and Lo and Weng (Ann. Inst. Statist. Math. 41 (1989) 227), for the Dirichlet and weighted gamma processes, respectively. The technique is based on a disintegration argument which reveals the role of a necessary positivity condition.

Suggested Citation

  • James, Lancelot F., 2003. "A simple proof of the almost sure discreteness of a class of random measures," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 363-368, December.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:363-368
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    Cited by:

    1. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    2. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Posterior analysis for some classes of nonparametric models," ICER Working Papers - Applied Mathematics Series 05-2008, ICER - International Centre for Economic Research.
    3. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97, March.
    4. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    5. Cerquetti, Annalisa, 2008. "On a Gibbs characterization of normalized generalized Gamma processes," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3123-3128, December.

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