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

TL;DR

This paper analyzes a complex two-color urn model with random sampling and reinforcement, providing growth rate results, estimators for reinforcement averages, and a CLT-based statistical test.

Contribution

It introduces a comprehensive analysis of a two-color urn with random multidrawing and non-balanced reinforcement, including growth rates, estimators, and a CLT-based testing method.

Findings

Identified exact growth rates of ball counts

Developed two consistent estimators for reinforcement averages

Proved a Central Limit Theorem for the model

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.