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An urn model with random multiple drawing and random addition

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  • Crimaldi, Irene
  • Louis, Pierre-Yves
  • Minelli, Ida G.

Abstract

We consider a two-color urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix is not balanced and it has general random entries. For the proportion of balls of a given color, we prove almost sure convergence results. In particular, in the case of equal reinforcement averages, we prove fluctuation theorems (through CLTs in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution) and we give asymptotic confidence intervals for the limit proportion, whose distribution is generally unknown.

Suggested Citation

  • Crimaldi, Irene & Louis, Pierre-Yves & Minelli, Ida G., 2022. "An urn model with random multiple drawing and random addition," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 270-299.
    • Handle: RePEc:eee:spapps:v:147:y:2022:i:c:p:270-299
    DOI: 10.1016/j.spa.2022.01.014
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    References listed on IDEAS

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    1. Benoit Laslier & Jean-François Laslier, 2017. "Reinforcement learning from comparisons: Three alternatives are enough, two are not," PSE-Ecole d'économie de Paris (Postprint) halshs-01630231, HAL.
    2. Patrizia Berti & Irene Crimaldi & Luca Pratelli & Pietro Rigo, 2010. "A Central Limit Theorem and Its Applications to Multicolor Randomly Reinforced Urns," Quaderni di Dipartimento 112, University of Pavia, Department of Economics and Quantitative Methods.
    3. Berti, Patrizia & Crimaldi, Irene & Pratelli, Luca & Rigo, Pietro, 2010. "Central limit theorems for multicolor urns with dominated colors," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1473-1491, August.
    4. Crimaldi, Irene & Dai Pra, Paolo & Minelli, Ida Germana, 2016. "Fluctuation theorems for synchronization of interacting Pólya’s urns," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 930-947.
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    Cited by:

    1. Crimaldi, Irene & Louis, Pierre-Yves & Minelli, Ida G., 2023. "Statistical test for an urn model with random multidrawing and random addition," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 342-360.

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