{
  "id": "0708.4294",
  "version": "v2",
  "published": "2007-08-31T08:20:25.000Z",
  "updated": "2008-05-21T12:10:38.000Z",
  "title": "Large sample asymptotics for the two-parameter Poisson--Dirichlet process",
  "authors": [
    "Lancelot F. James"
  ],
  "comment": "Published 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)",
  "journal": "IMS Collections 2008, Vol. 3, 187-199",
  "doi": "10.1214/074921708000000147",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "This paper explores large sample properties of the two-parameter $(\\alpha,\\theta)$ 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 $\\theta+n\\alpha.$ This latter result complements large $\\theta$ 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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-21T12:10:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G05",
      "62F15"
    ],
    "keywords": [
      "large sample asymptotics",
      "weak convergence",
      "two-parameter poisson-dirichlet posterior process",
      "result complements large",
      "properly centered two-parameter poisson-dirichlet processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.4294J"
    }
  }
}