The Annals of Statistics
- Ann. Statist.
- Volume 30, Number 5 (2002), 1376-1411.
Theory and numerical analysis for exact distributions of functionals of a Dirichlet process
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.
Ann. Statist., Volume 30, Number 5 (2002), 1376-1411.
First available in Project Euclid: 28 October 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62F15: Bayesian inference
Secondary: 60E15: Inequalities; stochastic orderings 62E17: Approximations to distributions (nonasymptotic)
Regazzini, Eugenio; Guglielmi, Alessandra; Di Nunno, Giulia. Theory and numerical analysis for exact distributions of functionals of a Dirichlet process. Ann. Statist. 30 (2002), no. 5, 1376--1411. doi:10.1214/aos/1035844980. https://projecteuclid.org/euclid.aos/1035844980