Clerico, Eugenio2025-10-212025-10-212025Clerico E. On the optimality of coin-betting for mean estimation. Int J Approx Reason. 2025 Dec;187:109550. DOI: 10.1016/j.ijar.2025.1095500888-613Xhttp://hdl.handle.net/10230/71603We 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.application/pdfeng© 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).info:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.ijar.2025.109550Sequential hypothesis testingE-variablesE-processesMean estimationAdmissibilityinfo:eu-repo/semantics/openAccess