UMVUE-Type Estimators under Bregman Losses
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910200818040832 |
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| author | Kamatsuka, Akira Watanabe, Shun |
| author_facet | Kamatsuka, Akira Watanabe, Shun |
| contents | We study unbiased estimation under Bregman losses and develop an extension of the classical theory of uniformly minimum variance unbiased estimators (UMVUEs). Exploiting bias--variance-type decompositions for Bregman divergences, we consider two natural loss functions, $D_φ(θ,\hatθ)$ and $D_φ(\hatθ,θ)$, and their corresponding notions of unbiasedness. We show that the latter formulation reduces to the classical setting, whereas the former yields a different framework in which unbiasedness is characterized in the dual space induced by $\nablaφ$. For the nontrivial case, we establish analogs of the Rao--Blackwell and Lehmann--Scheff{é} theorems, providing a systematic construction of type-I Bregman UMVUEs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_07426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | UMVUE-Type Estimators under Bregman Losses Kamatsuka, Akira Watanabe, Shun Information Theory We study unbiased estimation under Bregman losses and develop an extension of the classical theory of uniformly minimum variance unbiased estimators (UMVUEs). Exploiting bias--variance-type decompositions for Bregman divergences, we consider two natural loss functions, $D_φ(θ,\hatθ)$ and $D_φ(\hatθ,θ)$, and their corresponding notions of unbiasedness. We show that the latter formulation reduces to the classical setting, whereas the former yields a different framework in which unbiasedness is characterized in the dual space induced by $\nablaφ$. For the nontrivial case, we establish analogs of the Rao--Blackwell and Lehmann--Scheff{é} theorems, providing a systematic construction of type-I Bregman UMVUEs. |
| title | UMVUE-Type Estimators under Bregman Losses |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.07426 |