Theory and numerical analysis for exact distributions of functionals of a Dirichlet process
Eugenio Regazzini, Alessandra Guglielmi, Giulia Di Nunno
The Annals of Statistics · 2002 · Volume 30 · Issue 5
Abstract
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.
Keywords
60E15, 62E17, 62F15, Dirichlet process, distribution of (a vector of) linear functionals, numerical approximation of the exact distribution
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