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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.15077 |
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| _version_ | 1866909703061110784 |
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| author | Bhagwat, Pankaj Marchand, Eric |
| author_facet | Bhagwat, Pankaj Marchand, Eric |
| contents | For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $θ$ for cases where $θ> 0$, extending an earlier result of \cite{voinov1985unbiased} applicable to a normal model. We provide various applications for Gamma models, Inverse Gaussian models, distributions obtained by truncation, and ratios of normal means. Moreover, we extend the findings to estimating negative powers $θ^{-k}$, and more generally to complete monotone functions $q(θ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unbiased estimation in one-parameter exponential families for the inverse of the natural parameter with extensions Bhagwat, Pankaj Marchand, Eric Statistics Theory For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $θ$ for cases where $θ> 0$, extending an earlier result of \cite{voinov1985unbiased} applicable to a normal model. We provide various applications for Gamma models, Inverse Gaussian models, distributions obtained by truncation, and ratios of normal means. Moreover, we extend the findings to estimating negative powers $θ^{-k}$, and more generally to complete monotone functions $q(θ)$. |
| title | Unbiased estimation in one-parameter exponential families for the inverse of the natural parameter with extensions |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2507.15077 |