On statistics which are almost sufficient from the viewpoint of the Fisher metrics
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910458920828928 |
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| author | Yamaguchi, Kaori Nozawa, Hiraku |
| author_facet | Yamaguchi, Kaori Nozawa, Hiraku |
| contents | A statistic on a statistical model is sufficient if it has no information loss, namely, the Fisher metric of the induced model coincides with that of the original model due to Kullback and Ay-Jost-Lê-Schwachhöfer. We introduce a quantitatively weak version of sufficient statistics such that the Fisher metric of the induced model is bi-Lipschitz equivalent to that of the original model. We characterize such statistics in terms of the conditional probability or by the existence of a certain decomposition of the density function in a way similar to characterizations of sufficient statistics due to Fisher-Neyman and Ay-Jost-Lê-Schwachhöfer. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_04199 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On statistics which are almost sufficient from the viewpoint of the Fisher metrics Yamaguchi, Kaori Nozawa, Hiraku Statistics Theory Differential Geometry Probability A statistic on a statistical model is sufficient if it has no information loss, namely, the Fisher metric of the induced model coincides with that of the original model due to Kullback and Ay-Jost-Lê-Schwachhöfer. We introduce a quantitatively weak version of sufficient statistics such that the Fisher metric of the induced model is bi-Lipschitz equivalent to that of the original model. We characterize such statistics in terms of the conditional probability or by the existence of a certain decomposition of the density function in a way similar to characterizations of sufficient statistics due to Fisher-Neyman and Ay-Jost-Lê-Schwachhöfer. |
| title | On statistics which are almost sufficient from the viewpoint of the Fisher metrics |
| topic | Statistics Theory Differential Geometry Probability |
| url | https://arxiv.org/abs/2305.04199 |