{
  "abstract": "First-order minimaxity offers limited guidance for choosing among global-local shrinkage priors, since different local-tail distributions can yield the same leading risk. Comparisons at a common global scale may also be misleading, as the scale interacts with the shape of the local prior. We study the worst-case squared-error risks of posterior means in sparse Gaussian normal-means estimation, allowing each prior its own risk-minimizing global scale. For local-variance priors with polynomial tails and logarithmic corrections, we characterize the calibrations that retain first- and second-order minimaxity and derive the asymptotic form of the unrestricted oracle scale. Even after this optimization, differences in risk remain. The polynomial tail index, logarithmic tail exponent and a scale-invariant higher-order correction distinguish priors at successively finer orders. In particular, the horseshoe has smaller asymptotic oracle risk than the horseshoe+, despite the latter's additional logarithmic tail factor. We also establish the calibration accuracy needed to preserve these differences and sufficient conditions for their stability under high-dimensional Gaussian regression designs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24352",
  "author_total": 1,
  "authors": [
    {
      "name": "Dongu Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jqvfbjd79433.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24352",
  "fulltext_url": null,
  "id": "5jqvfbjd79433",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24352",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7223031819",
  "pdf_url": "https://arxiv.org/pdf/2610.24352",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jqvfbjd79433.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2610.24352",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24352"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Higher Order Risk Comparisons of Oracle Calibrated Global Local Priors",
  "title_text": "Higher Order Risk Comparisons of Oracle Calibrated Global Local Priors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/5jqvfbjd79433",
  "venue": "arXiv",
  "versions": []
}