eprintid: 2129
rev_number: 5
eprint_status: archive
userid: 36
dir: disk0/00/00/21/29
datestamp: 2014-02-04 08:35:44
lastmod: 2014-02-04 08:35:44
status_changed: 2014-02-04 08:35:44
type: article
succeeds: 1544
metadata_visibility: no_search
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 an Indian Buffet Model with Random Weights
ispublished: inpress
subjects: HA
subjects: QA
divisions: EIC
full_text_status: none
monograph_type: technical_report
keywords: Bayesian nonparametrics, Central limit theorem, Conditional identity in distribution, Indian buffet process, Random measure, Random reinforcement, Stable convergence
note: Forthcoming
abstract: The three-parameter Indian buffet process is generalized. T
he possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let L_n be the number of dishes experimented by the first n customers, and let 
{\bar K}_n=(1/n)\sum_{i=1}^n K_i
where K_i is the number of dishes tried by customer i. The asymptotic distributions of L_n and {\bar K}_n, suitably
centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., non generalized) Indian buffet process.
date: 2014
date_type: published
publication: The Annals of Applied Probability
number:  
pages: 17
institution: IMT Institute for Advanced Studies Lucca
refereed: TRUE
issn: 1050-5164
official_url: http://www.imstat.org/aap/future_papers.html
citation:   Berti, Patrizia and Crimaldi, Irene and Pratelli, Luca and Rigo, Pietro  Central Limit Theorems for an Indian Buffet Model with Random Weights.  The Annals of Applied Probability ( ).   ISSN 1050-5164    (In Press)   (2014)