{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.07426",
  "author_total": 2,
  "authors": [
    {
      "name": "Akira Kamatsuka"
    },
    {
      "name": "Shun Watanabe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx8nhg2h6k767.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.07426",
  "fulltext_url": null,
  "id": "fx8nhg2h6k767",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.07426",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7160875392",
  "pdf_url": "https://arxiv.org/pdf/2605.07426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx8nhg2h6k767.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2605.07426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.07426"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Methods and Inference",
      "subfield": "statistics"
    }
  ],
  "title": "UMVUE-Type Estimators under Bregman Losses",
  "title_text": "UMVUE-Type Estimators under Bregman Losses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/fx8nhg2h6k767",
  "venue": "arXiv",
  "versions": []
}