Minimaxity under the half-Cauchy prior
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909223158284288 |
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| author | Maruyama, Yuzo Matsuda, Takeru |
| author_facet | Maruyama, Yuzo Matsuda, Takeru |
| contents | This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the quadratic loss, they demonstrated that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In this paper, we theoretically establish the minimaxity of the corresponding Bayes estimator using the interval arithmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimaxity under the half-Cauchy prior Maruyama, Yuzo Matsuda, Takeru Statistics Theory 62C20 This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the quadratic loss, they demonstrated that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In this paper, we theoretically establish the minimaxity of the corresponding Bayes estimator using the interval arithmetric. |
| title | Minimaxity under the half-Cauchy prior |
| topic | Statistics Theory 62C20 |
| url | https://arxiv.org/abs/2406.08892 |