{
  "abstract": "Elliptical distributions provide a flexible and widely used extension of multivariate normal distribution. They play a critical role in many statistical procedures when dealing with high-dimensional data. However, goodness-of-fit testing for elliptical distributions remains challenging when the dimension $p$ is comparable to or larger than the sample size $n$. In this work, we propose a new test for high-dimensional elliptical distributions. We establish high-dimensional Gaussian approximation for the test statistic under general correlation structures, allowing the dimension to grow as \\(\\log p=o(n^{1/14})\\) under finite moment conditions. We further develop Gaussian multiplier bootstrap test procedure and prove its theoretical validity. Numerical studies demonstrate stable finite-sample behavior and favorable power against a range of alternatives. Applications to real datasets illustrate practical utility of the proposed test.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11304",
  "author_total": 4,
  "authors": [
    {
      "name": "Wenrui Wu"
    },
    {
      "name": "Bingye Yang"
    },
    {
      "name": "Minghua Deng"
    },
    {
      "name": "Xu Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ae3d5v4nn91e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11304",
  "fulltext_url": null,
  "id": "7ae3d5v4nn91e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11304",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7168265006",
  "pdf_url": "https://arxiv.org/pdf/2607.11304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ae3d5v4nn91e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2607.11304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11304"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "A New Test for High-Dimensional Elliptical Distributions",
  "title_text": "A New Test for High-Dimensional Elliptical Distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/7ae3d5v4nn91e",
  "venue": "arXiv",
  "versions": []
}