{
  "abstract": "We study the mean estimation of Gaussian location model with star-shaped constraints under adversarial contamination, where at most $ k<N/2 $ among $ N $ observations are corrupted by an oracle adversary. We characterize the minimax squared $ \\ell_2 $ risk throughout the full range of contamination level $ \\varepsilon = k/N \\in [0,1/2) $. The minimax risk is \\begin{equation*} \\mathfrak{M}\\asymp \\big( δ_\\varepsilon ^{*2} \\vee σ^2\\varepsilon ^2\\log \\frac{e}{1-2\\varepsilon } \\big) \\wedge d^2 , \\end{equation*} where $ δ_\\varepsilon ^* := \\sup \\big\\{ r \\geq 0: (1-2\\varepsilon )\\frac{Nr ^2}{σ^2} \\leq \\log M^\\mathrm{ loc }_K(r ,c) \\big\\} $, $ \\log M^\\mathrm{ loc }_K(r ,c) $ is the local entropy of constraint set $ K $, $ d $ is the diameter of $ K $ (set $ d=\\infty $ if $ K $ is unbounded), $ σ^2 I_n $ is the covariance of the Gaussian noise, and $ c $ is a sufficiently large constant. Our result sheds light on the interaction between contamination error and information theoretic complexity in the regime of proximity to the breakdown point $ \\varepsilon \\uparrow 1/2 $.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36283",
  "author_total": 2,
  "authors": [
    {
      "name": "Tuorui Peng"
    },
    {
      "name": "Matey Neykov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0mtk8gt2b3v0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36283",
  "fulltext_url": null,
  "id": "f0mtk8gt2b3v0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36283",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Statistical Methods and Models"
    ]
  ],
  "openalex": "W7224091617",
  "pdf_url": "https://arxiv.org/pdf/2610.36283",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0mtk8gt2b3v0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36283",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36283"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Minimax Rates for Robust Gaussian Mean Estimation Near the Breakdown Point under Constraints",
  "title_text": "Minimax Rates for Robust Gaussian Mean Estimation Near the Breakdown Point under Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/f0mtk8gt2b3v0",
  "venue": "arXiv",
  "versions": []
}