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PreprintarXiv licencearXiv

UMVUE-Type Estimators under Bregman Losses

  • Akira Kamatsuka
  • Shun Watanabe
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Abstract

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, Dφ(θ,θ̂) and Dφ(θ̂,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 ∇φ. 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.

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Cite

BibTeXRIS
BibTeX
@misc{kamatsuka2026umvuetype,
  title = {{UMVUE-Type Estimators under Bregman Losses}},
  author = {Akira Kamatsuka and Shun Watanabe},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2605.07426},
  eprint = {2605.07426},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.07426},
}
RIS
TY  - UNPB
TI  - UMVUE-Type Estimators under Bregman Losses
AU  - Akira Kamatsuka
AU  - Shun Watanabe
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2605.07426
UR  - https://arxiv.org/abs/2605.07426
AB  - 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,θ̂) and D_φ(θ̂,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 ∇φ. 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.
ER  -