UMVUE-Type Estimators under Bregman Losses

Akira Kamatsuka; Shun Watanabe

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arXiv · 2605.07426

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, $D_φ(θ,\hatθ)$ 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.

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Akira Kamatsuka, Shun Watanabe. 2026-08-31. UMVUE-Type Estimators under Bregman Losses. https://arxiv.org/abs/2605.07426

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