Context-sensitive hypothesis-testing and exponential families
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914892927205376 |
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| author | Kelbert, Mark Suhov, Yuri |
| author_facet | Kelbert, Mark Suhov, Yuri |
| contents | We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted information and weighted entropy that proved useful in industrial/microeconomic and medical statistics. We focus on applications relevant in hypothesis testing and an analysis of exponential families. Several notions, bounds and asymptotics are established, which generalize their counterparts well-known in standard statistical research. It includes Stein-Sanov theorem, Pinsker's, Bretangnole-Huber and van Trees inequalities and Kullback--Leibler, Bhattacharya, Bregman, Burbea-Rao, Chernoff, Renyi and Tsallis divergences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Context-sensitive hypothesis-testing and exponential families Kelbert, Mark Suhov, Yuri Statistics Theory 62C05, 62F03, 62F10 We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted information and weighted entropy that proved useful in industrial/microeconomic and medical statistics. We focus on applications relevant in hypothesis testing and an analysis of exponential families. Several notions, bounds and asymptotics are established, which generalize their counterparts well-known in standard statistical research. It includes Stein-Sanov theorem, Pinsker's, Bretangnole-Huber and van Trees inequalities and Kullback--Leibler, Bhattacharya, Bregman, Burbea-Rao, Chernoff, Renyi and Tsallis divergences. |
| title | Context-sensitive hypothesis-testing and exponential families |
| topic | Statistics Theory 62C05, 62F03, 62F10 |
| url | https://arxiv.org/abs/2407.20894 |