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VOL. 3 | 2008 Large sample asymptotics for the two-parameter Poisson–Dirichlet process

Abstract

This paper explores large sample properties of the two-parameter (α, θ) Poisson–Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension of the Dirichlet process, we explore the consistency and weak convergence of the the two-parameter Poisson–Dirichlet posterior process. We also establish the weak convergence of properly centered two-parameter Poisson–Dirichlet processes for large θ+. This latter result complements large θ results for the Dirichlet process and Poisson–Dirichlet sequences, and complements a recent result on large deviation principles for the two-parameter Poisson–Dirichlet process. A crucial component of our results is the use of distributional identities that may be useful in other contexts.

Information

Published: 1 January 2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2459225

Digital Object Identifier: 10.1214/074921708000000147

Subjects:
Primary: 62G05
Secondary: 62F15

Keywords: Bayesian consistency , multiplier CLT , two-parameter Poisson–Dirichlet process , weak convergence

Rights: Copyright © 2008, Institute of Mathematical Statistics

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