Bahadur asymptotic efficiency in the zone of moderate deviation probabilities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914441049669632 |
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| author | Ermakov, Mikhail |
| author_facet | Ermakov, Mikhail |
| contents | For a sequence of independent identically distributed random variables having a distribution function with an unknown parameter from a set $Θ\subset \mathbf{R}^d$, we prove an analogue of the lower bound of Bahadur asymptotic efficiency for the zone of moderate deviation probabilities. The assumptions coincide with assumptions conditions under which the locally asymptotically minimax lower bound of Hajek-Le Cam was proved. The lower bound for local Bahadur asymptotic efficiency is a special case of this lower bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19331 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bahadur asymptotic efficiency in the zone of moderate deviation probabilities Ermakov, Mikhail Statistics Theory 62F10, 62F12 For a sequence of independent identically distributed random variables having a distribution function with an unknown parameter from a set $Θ\subset \mathbf{R}^d$, we prove an analogue of the lower bound of Bahadur asymptotic efficiency for the zone of moderate deviation probabilities. The assumptions coincide with assumptions conditions under which the locally asymptotically minimax lower bound of Hajek-Le Cam was proved. The lower bound for local Bahadur asymptotic efficiency is a special case of this lower bound. |
| title | Bahadur asymptotic efficiency in the zone of moderate deviation probabilities |
| topic | Statistics Theory 62F10, 62F12 |
| url | https://arxiv.org/abs/2504.19331 |