eprintid: 2612
rev_number: 4
eprint_status: archive
userid: 36
dir: disk0/00/00/26/12
datestamp: 2015-02-23 08:34:38
lastmod: 2015-02-23 08:34:38
status_changed: 2015-02-23 08:34:38
type: article
succeeds: 2129
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 an Indian Buffet Model with Random Weights
ispublished: pub
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
abstract: The three-parameter Indian buffet process is generalized. The 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: 2015
date_type: published
publication: The Annals of Applied Probability
volume: 25
number: 2
publisher: Institute of Mathematical Statistics
pagerange: 523-547
pages: 17
id_number: DOI: 10.1214/14-AAP1002
institution: IMT Institute for Advanced Studies Lucca
refereed: TRUE
issn: 1050-5164
official_url: http://projecteuclid.org/euclid.aoap/1424355122
related_url_url: http://www.imstat.org/aap/
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, 25 (2).  pp. 523-547.  ISSN 1050-5164      (2015)