On the optimality of coin-betting for mean estimation

Eugenio Clerico

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arXiv · 2412.02640

On the optimality of coin-betting for mean estimation

Eugenio Clerico

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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.

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Eugenio Clerico. 2024-12-03. On the optimality of coin-betting for mean estimation. https://arxiv.org/abs/2412.02640

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