On the optimality of coin-betting for mean estimation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913097622487040 |
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| author | Clerico, Eugenio |
| author_facet | Clerico, Eugenio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the optimality of coin-betting for mean estimation Clerico, Eugenio Statistics Theory Methodology 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. |
| title | On the optimality of coin-betting for mean estimation |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2412.02640 |