Theory and numerical analysis for exact distributions of functionals of a Dirichlet process

• 成果类型: Article
• 署名作者: Regazzini, E; Guglielmi, A; Di Nunno, G
• 署名单位: University of Pavia; Consiglio Nazionale delle Ricerche (CNR)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 1376-1411
• 关键词: inference; inversion

摘要

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.