eprintid: 978
rev_number: 9
eprint_status: archive
userid: 36
dir: disk0/00/00/09/78
datestamp: 2011-10-31 12:04:05
lastmod: 2011-11-03 13:19:36
status_changed: 2011-10-31 12:04:05
type: article
metadata_visibility: show
creators_name: Berti, Patrizia
creators_name: Crimaldi, Irene
creators_name: Pratelli, Luca
creators_name: Rigo, Pietro
creators_id: 
creators_id: irene.crimaldi@imtlucca.it
creators_id: 
creators_id: 
title: Central limit theorems for multicolor urns with dominated colors
ispublished: pub
subjects: HA
subjects: QA
divisions: EIC
full_text_status: public
keywords: Central limit theorem; Clinical trials; Random probability measure; Stable convergence; Urn model
abstract: An urn contains balls of d≥2 colors. At each time n≥1, a ball is drawn and then replaced together with a random number of balls of the same color. Let A n = diag (An,1,…,An,d) be the n-th reinforce matrix. Assuming that EAn,j=EAn,1 for all n and j, a few central limit theorems (CLTs) are available for such urns. In real problems, however, it is more reasonable to assume that EA n,j = EA n,1 whenever  n ≥ 1  and  1 ≤ j ≤ d0 , liminfn EAn,1 > limsupn EAn,j whenever  j > d0  for some integer 1≤d0≤d. Under this condition, the usual weak limit theorems may fail, but it is still possible to prove the CLTs for some slightly different random quantities. These random quantities are obtained by neglecting dominated colors, i.e., colors from d0+1 to d, and they allow the same inference on the urn structure. The sequence (An : n ≥ 1) is independent but need not be identically distributed. Some statistical applications are given as well.
date: 2010-08
date_type: published
publication: Stochastic processes and their applications 
volume: 120
number: 8
publisher: Elsevier
pagerange: 1473-1491
id_number: 10.1016/j.spa.2010.04.005
refereed: TRUE
issn: 0304-4149
official_url: http://www.sciencedirect.com/science/article/pii/S0304414910001109
citation:   Berti, Patrizia and Crimaldi, Irene and Pratelli, Luca and Rigo, Pietro  Central limit theorems for multicolor urns with dominated colors.  Stochastic processes and their applications , 120 (8).  pp. 1473-1491.  ISSN 0304-4149      (2010)  
document_url: http://eprints.imtlucca.it/978/1/Cirmaldi_2010.pdf