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Statistical test for an urn model with random multidrawing and random addition

Author

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

Abstract

We complete the study of the model introduced in Crimaldi et al., (2022). It is a two-color urn model with multiple drawing and random (non-balanced) time-dependent reinforcement matrix. The number of sampled balls at each time-step is random. We identify the exact rates at which the number of balls of each color grows to +∞ and define two strongly consistent estimators for the limiting reinforcement averages. Then we prove a Central Limit Theorem, which allows to design a statistical test for such averages.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:158:y:2023:i:c:p:342-360
    DOI: 10.1016/j.spa.2022.12.012
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    References listed on IDEAS

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    1. Crimaldi, Irene & Pratelli, Luca, 2005. "Convergence results for multivariate martingales," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 571-577, April.
    2. 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.
    3. 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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