{
  "abstract": "For estimating the mean vector of a $p$-variate normal distribution ($p \\ge 3$) under quadratic loss, the positive-part James-Stein estimator dominates the original Jame-Stein estimator though it suffers from a non-smooth thresholding boundary. In this paper, we first express the shrinkage factor of the positive-part estimator using an infinite series. Truncating this series at a finite degree $m$ allows us to interpret the factor as a special case of $q$-numbers. Leveraging these $q$-numbers parameterized by a positive real index $m$, we propose a novel smooth estimator. We prove that the proposed estimator dominates the original James-Stein estimator for any dimension $p \\ge 3$, provided the truncation parameter satisfies $m \\ge 0.95\\sqrt{p-2}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39614",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuzo Maruyama"
    },
    {
      "name": "Akimichi Takemura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1b15vhwqmwft.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39614",
  "fulltext_url": null,
  "id": "d1b15vhwqmwft",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39614",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7215117665",
  "pdf_url": "https://arxiv.org/pdf/2609.39614",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1b15vhwqmwft.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.39614",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39614"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Improving the James-Stein estimator via q-number shrinkage",
  "title_text": "Improving the James-Stein estimator via q-number shrinkage",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/d1b15vhwqmwft",
  "venue": "arXiv",
  "versions": []
}