Electronic Journal of Statistics

A vector of Dirichlet processes

Fabrizio Leisen, Antonio Lijoi, and Dario Spanó

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Abstract

Random probability vectors are of great interest especially in view of their application to statistical inference. Indeed, they can be used for identifying 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 the construction of a vector of Dirichlet processes based on the normalization of an exchangeable vector of completely random measures that are jointly infinitely divisible. After deducing the form of the multivariate Laplace exponent associated to the vector of the gamma completely random measures, we analyze some of their distributional properties. Our attention particularly focuses on the dependence structure and the specific partition probability function induced by the proposed vector.

Article information

Source
Electron. J. Statist., Volume 7 (2013), 62-90.

Dates
First available in Project Euclid: 11 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1357913282

Digital Object Identifier
doi:10.1214/12-EJS764

Mathematical Reviews number (MathSciNet)
MR3020414

Zentralblatt MATH identifier
1328.60124

Keywords
Bayesian nonparametrics completely random measure Dirichlet process Lévy copula multivariate Lévy measure partial exchangeability partition probability function

Citation

Leisen, Fabrizio; Lijoi, Antonio; Spanó, Dario. A vector of Dirichlet processes. Electron. J. Statist. 7 (2013), 62--90. doi:10.1214/12-EJS764. https://projecteuclid.org/euclid.ejs/1357913282


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