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Central limit theorems for a hypergeometric randomly reinforced urn

Crimaldi, Irene Central limit theorems for a hypergeometric randomly reinforced urn. Journal of applied probability, 53 (3). pp. 899-913. ISSN 0021-9002 (2016)

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We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color given the past is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution. The proven results provide asymptotic confidence intervals for the limit proportion, whose distribution is generally unknown. Moreover, we also consider the case of more urns subjected to some random common factors.

Item Type: Article
Identification Number: 10.1017/jpr.2016.48
Projects: Crisis Lab
Uncontrolled Keywords: Central limits; Polya urn; Randomly reinforced urn; stable convergence
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Research Area: Economics and Institutional Change
Depositing User: Caterina Tangheroni
Date Deposited: 14 Nov 2016 11:56
Last Modified: 14 Nov 2016 11:56
URI: http://eprints.imtlucca.it/id/eprint/3597

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