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

2022/06/11 by Irene Crimaldi, Crimaldi, Irene, Pierre‐Yves Louis +3
Mathematics · #60B10 #60F05 #60F15 #60G42 #62P25 #91D30 #92C60 #FOS: Mathematics #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2206.05515

openalex publication_date 2022/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We complete the study of the model introduced in [11]. 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 infinity 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.

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• Unbalanced urn model with random addition
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• On generalized Pólya urn models
• Central limit Theorem for an Adaptive Randomly Reinforced Urn Model