Crimaldi, Irene Central limit theorems for a hypergeometric randomly reinforced urn. Technical Report arXiv (Submitted)
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Abstract
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: | Working Paper (Technical Report) |
|---|---|
| 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 11:52 |
| Last Modified: | 14 Nov 2016 11:52 |
| URI: | http://eprints.imtlucca.it/id/eprint/3596 |
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- Central limit theorems for a hypergeometric randomly reinforced urn. (deposited 14 Nov 2016 11:52) [Currently Displayed]
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