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A multivariate extension of a vector of Poisson- Dirichlet processes

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  • W. Zhu

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  • Frabrizio Leisen

    ()

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    Abstract

    Recently, Leisen and Lijoi (2011) introduced a bivariate vector of random probability measures with Poisson-Dirichlet marginals where the dependence is induced through a Lévy's Copula. In this paper the same approach is used for generalizing such a vector to the multivariate setting. Some non-trivial results are proved in the multidimensional case, in particular, the Laplace transform and the Exchangeable Partition Probability function (EPPF). Finally, some numerical illustrations of the EPPF are provided

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    File URL: http://e-archivo.uc3m.es/bitstream/10016/17179/1/ws132220.pdf
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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws132220.

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    Date of creation: Jun 2013
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    Handle: RePEc:cte:wsrepe:ws132220

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    Related research

    Keywords: Bayesian inference; Dirichlet process; Vectors of Poisson-Dirichlet processes; Multivariate Lévy measure; Partial exchangeability; Partition probability function;

    This paper has been announced in the following NEP Reports:

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    1. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    2. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    3. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Controlling the reinforcement in Bayesian non-parametric mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 715-740.
    4. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    5. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
    6. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
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