relation: http://eprints.imtlucca.it/975/
title: A central limit theorem and its applications to multicolor randomly reinforced urns
creator: Berti, Patrizia
creator: Crimaldi, Irene
creator: Pratelli, Luca
creator: Rigo, Pietro
subject: HA Statistics
subject: QA Mathematics
description: Let Xn be a sequence of integrable real random variables, adapted to a filtration (Gn). Define Cn = √{(1 / n)∑k=1nXk - E(Xn+1 | Gn)} and Dn = √n{E(Xn+1 | Gn) - Z}, where Z is the almost-sure limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn, Dn) → N(0, U) x N(0, V) stably are given, where U and V are certain random variables. In particular, under such conditions, we obtain √n{(1 / n)∑k=1nX_k - Z} = Cn + Dn → N(0, U + V) stably. This central limit theorem has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced urns. 
publisher: Applied Probability Trust
date: 2011
type: Article
type: PeerReviewed
identifier:   Berti, Patrizia and Crimaldi, Irene and Pratelli, Luca and Rigo, Pietro  A central limit theorem and its applications to multicolor randomly reinforced urns.  Journal of applied probability , 48 (2).  pp. 527-546.  ISSN 0021-9002      (2011)  
relation: http://projecteuclid.org/euclid.jap/1308662642
relation: 10.1239/jap/1308662642