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October 2002 Theory and numerical analysis for exact distributions of functionals of a Dirichlet process
Eugenio Regazzini, Alessandra Guglielmi, Giulia Di Nunno
Ann. Statist. 30(5): 1376-1411 (October 2002). DOI: 10.1214/aos/1035844980


The distribution of a mean or, more generally, of a vector of means of a Dirichlet process is considered. Some characterizing aspects of this paper are: (i) a review of a few basic results, providing new formulations free from many of the extra assumptions considered to date in the literature, and giving essentially new, simpler and more direct proofs; (ii) new numerical evaluations, with any prescribed error of approximation, of the distribution at issue; (iii) a new form for the law of a vector of means. Moreover, as applications of these results, we give: (iv) the sharpest condition sufficient for the distribution of a mean to be symmetric; (v) forms for the probability distribution of the variance of the Dirichlet random measure; (vi) some hints for determining the finite-dimensional distributions of a random function connected with Bayesian methods for queuing models.


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Eugenio Regazzini. Alessandra Guglielmi. Giulia Di Nunno. "Theory and numerical analysis for exact distributions of functionals of a Dirichlet process." Ann. Statist. 30 (5) 1376 - 1411, October 2002.


Published: October 2002
First available in Project Euclid: 28 October 2002

zbMATH: 1018.62011
MathSciNet: MR1936323
Digital Object Identifier: 10.1214/aos/1035844980

Primary: 62F15
Secondary: 60E15 , 62E17

Keywords: Dirichlet process , distribution of (a vector of) linear functionals , numerical approximation of the exact distribution

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 5 • October 2002
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