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)
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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.
| Item Type: | Article |
|---|---|
| Additional Information: | Forthcoming |
| Uncontrolled Keywords: | Bayesian nonparametrics, Central limit theorem, Conditional identity in distribution, Indian buffet process, Random measure, Random reinforcement, Stable convergence |
| Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
| Research Area: | Economics and Institutional Change |
| Depositing User: | Irene Crimaldi |
| Date Deposited: | 04 Feb 2014 08:35 |
| Last Modified: | 04 Feb 2014 08:35 |
| URI: | http://eprints.imtlucca.it/id/eprint/2129 |
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Central Limit Theorems for an Indian Buffet Model with Random Weights. (deposited 16 Apr 2013 14:59)
- Central Limit Theorems for an Indian Buffet Model with Random Weights. (deposited 04 Feb 2014 08:35) [Currently Displayed]
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