{
  "abstract": "We study identity testing for high-dimensional covariance matrices against dense alternatives of unknown direction, with $p/n \\to γ$. Along a globally positive quadratic precision path, mixing Gaussian alternatives over a Gaussian Orthogonal Ensemble direction yields a contiguous experiment whose log likelihood reduces to the corrected Frobenius statistic; its upper-tail test attains the limiting weighted-power envelope at every fixed strength. Fixing the prior's Frobenius radius perturbs the mixture by only $O(p^{-1/2})$ in total variation, and exact whitening carries the experiment, the statistic, and its null law to any known null covariance. Separately, under a product-coordinate null, feasibility needs only $4+η$ moments, plus identical distributions over time when means are estimated; studentization and an exact degrees-of-freedom correction preserve the local power. A stability inequality turns near-envelope attainment into null agreement with the Frobenius rule, so uniform noninferiority on the typical dense bulk precludes gains at any contiguous alternative. For trace-matched rank-one alternatives, the corrected statistic is the first likelihood direction when $\\vartheta_n \\to 0$ and $n\\vartheta_n \\to \\infty$; at fixed strength, the log likelihood ratio in the Onatski-Moreira-Hallin fixed-spike benchmark is governed by a richer linear spectral statistic below the Baik-Ben Arous-Peche threshold, while eigenvalue separation permits cost-free largest-eigenvalue enhancement above it. Simulations illustrate the theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27200",
  "author_total": 3,
  "authors": [
    {
      "name": "Peter Reinhard Hansen"
    },
    {
      "name": "Werner Ploberger"
    },
    {
      "name": "Chen Tong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6spyd5tsses4j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27200",
  "fulltext_url": null,
  "id": "6spyd5tsses4j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27200",
  "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",
      "econ.EM"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214144988",
  "pdf_url": "https://arxiv.org/pdf/2609.27200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6spyd5tsses4j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Local Optimality and Rigidity of Frobenius Tests for Dense High-Dimensional Covariance Alternatives",
  "title_text": "Local Optimality and Rigidity of Frobenius Tests for Dense High-Dimensional Covariance Alternatives",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/6spyd5tsses4j",
  "venue": "arXiv",
  "versions": []
}