{
  "abstract": "We obtain a near-minimax rate on covariance estimation of adversarially corrupted Gaussian data in Frobenius norm when the covariance estimation is assumed to lie in a star-shaped set $K \\subseteq \\mathbb{R}^{n \\times n}$. Assuming a known upper bound of $\\varepsilon < 1/32$ on the fraction of the $N$ observations of data $X$ are arbitrarily corrupted by an omniscient adversary, we obtain the near-minimax rate (up to constants) of \\begin{align*} \\left(\\varepsilon^2 \\vee δ^{\\star2} \\right)\\wedge d^2 \\lesssim \\inf_{\\hatΣ} \\sup_{Σ\\in K} \\sup_{\\mathrm{C}} \\mathbb{E} \\| \\hatΣ(\\mathrm{C}(X)) - Σ\\|_F^2 \\lesssim \\left(\\varepsilon^2\\log^2(1/\\varepsilon) \\vee δ^{\\star2} \\right)\\wedge d^2 \\end{align*} where $d$ is the diameter of the set $K$, $N \\gtrsim \\sup_{δ> 0} \\log \\mathrm{M}^{\\operatorname{loc}}(δ, 2c)$, and \\begin{align*} δ^*=\\sup\\left\\{ δ\\geq 0: \\frac{N}{Υ^2} δ^2\\leq \\log \\mathrm{M}_K^{\\operatorname{loc}}(δ,c) \\right\\} \\end{align*} for an arbitrary large constant $c$ and the local metric entropy of $K$, $\\mathrm{M}^{\\operatorname{loc}}_K(δ,c)$. We believe this is the first such general result on structured robust covariance estimation in the Frobenius norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10840",
  "author_total": 3,
  "authors": [
    {
      "name": "Samuel Ozminkowski"
    },
    {
      "name": "Hongmei Jiang"
    },
    {
      "name": "Matey Neykov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6m3kyfvxm5320.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10840",
  "fulltext_url": null,
  "id": "6m3kyfvxm5320",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10840",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Statistical Methods and Models"
    ]
  ],
  "openalex": "W7221153395",
  "pdf_url": "https://arxiv.org/pdf/2610.10840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6m3kyfvxm5320.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Statistical Guarantees for Covariance Estimation with Adversarial Corruption under Constraints",
  "title_text": "Statistical Guarantees for Covariance Estimation with Adversarial Corruption under Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/6m3kyfvxm5320",
  "venue": "arXiv",
  "versions": []
}