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, $D_{\varphi}(\theta,\hat{\theta})$ and $D_{\varphi}(\hat{\theta},\theta)$, 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 $\nabla\varphi$. 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.
From: Akira Kamatsuka [view email]
[v1]
Fri, 8 May 2026 08:22:57 UTC (78 KB)
[v2]
Mon, 31 Aug 2026 14:00:12 UTC (79 KB)
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