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A vector of Dirichlet processes


  • Leisen, Fabrizio
  • Lijoi, Antonio
  • Spanó, Dario


Random probability vectors are of great interest especially in view of their application to statistical inference. Indeed, they can be used for determining the de Finetti mixing measure in the representation of the law of a partially exchangeable array of random elements taking values in a separable and complete metric space. In this paper we describe a construction of a vector of Dirichlet processes based on the normalization of completely random measures that are jointly infinitely divisible. After deducing the form of the Laplace exponent of the vector of the gamma completely random measures, we study some of their distributional properties. Our attention particularly focuses on the dependence structure and the specific partition probability function induced by the proposed vector.

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  • Leisen, Fabrizio & Lijoi, Antonio & Spanó, Dario, 2012. "A vector of Dirichlet processes," DES - Working Papers. Statistics and Econometrics. WS ws122115, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws122115

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    References listed on IDEAS

    1. Tehranchi, Michael R., 2009. "Symmetric martingales and symmetric smiles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3785-3797, October.
    2. Ilya Molchanov & Michael Schmutz, 2009. "Exchangeability type properties of asset prices," Papers 0901.4914,, revised Apr 2011.
    3. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Papers 0809.0301,, revised Nov 2009.
    4. Molchanov, Ilya, 2009. "Convex and star-shaped sets associated with multivariate stable distributions, I: Moments and densities," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2195-2213, November.
    5. K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, EconWPA.
    6. Stoev, Stilian A., 2008. "On the ergodicity and mixing of max-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1679-1705, September.
    7. Hardin, Clyde D., 1982. "On the spectral representation of symmetric stable processes," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 385-401, September.
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    Bayesian inference;

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