Large sample asymptotics for the two-parameter Poisson--Dirichlet process

Simple item page
dc.creatorJames, Lancelot F.
dc.date2007-08-31
dc.date2008-05-21
dc.date.accessioned2026-07-07T09:39:46Z
dc.date.available2026-07-07T09:39:46Z
dc.descriptionThis 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 $θ+nα.$ 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/074921708000000147 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0708.4294
dc.identifierhttp://arxiv.org/abs/0708.4294
dc.identifierIMS Collections 2008, Vol. 3, 187-199
dc.identifierdoi:10.1214/074921708000000147
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161298
dc.subjectProbability
dc.subjectStatistics Theory
dc.subject62G05 (Primary) 62F15 (Secondary)
dc.titleLarge sample asymptotics for the two-parameter Poisson--Dirichlet process
dc.typetext

Files

Collections

arXiv