On the optimality of coin-betting for mean estimation

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• dc.contributor.author Clerico, Eugenio
• dc.date.accessioned 2025-10-21T05:48:35Z
• dc.date.available 2025-10-21T05:48:35Z
• dc.date.issued 2025
• dc.description.abstract 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.en
• dc.description.sponsorship The author would like to thank Gergely Neu, Peter D. Grünwald, Nishant A. Mehta, Hamish E. Flynn, and Claudia M. Chanu, for the insightful discussions that inspired this work. I would also like to thank Nick W. Koning and Aditya Ramdas for their constructive feedback, which helped improve this work following its initial appearance, and Wouter M. Koolen for helpful discussions on e-processes. Finally, I thank the anonymous reviewers for the insightful comments and feedback that helped improving this work. GPT-4o was used during the redaction of this paper to polish the presentation. All AI-generated text was reviewed and edited by the author, who takes full responsibility for the content of this manuscript. This project was funded by the European Research Council (ERC), under the European Union's Horizon 2020 research and innovation programme (grant agreement 950180).en
• dc.format.mimetype application/pdf
• dc.identifier.citation Clerico E. On the optimality of coin-betting for mean estimation. Int J Approx Reason. 2025 Dec;187:109550. DOI: 10.1016/j.ijar.2025.109550
• dc.identifier.doi http://dx.doi.org/10.1016/j.ijar.2025.109550
• dc.identifier.issn 0888-613X
• dc.identifier.uri http://hdl.handle.net/10230/71603
• dc.language.iso eng
• dc.publisher Elsevier
• dc.relation.ispartof International Journal of Approximate Reasoning. 2025 Dec;187:109550
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/950180
• dc.rights © 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/).
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Sequential hypothesis testingen
• dc.subject.keyword E-variablesen
• dc.subject.keyword E-processesen
• dc.subject.keyword Mean estimationen
• dc.subject.keyword Admissibilityen
• dc.title On the optimality of coin-betting for mean estimationen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion