2024/12/03 by Eugenio Clerico, Clerico, Eugenio · 1 voice · 1 citation
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Modeling, Simulation, and Optimization #math.ST #stat.ME
paper · pdf · doi:10.48550/arxiv.2412.02640
openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimality of the coin-betting formulation among e-variable-based algorithmic frameworks for testing and estimating the (conditional) mean. As a consequence, we provide a direct and explicit characterisation of all valid e-variables and e-processes for this testing problem. In the language of classical statistical decision theory, we fully describe the set of all admissible e-variables and e-processes, and identify the corresponding minimal complete class.