{
  "abstract": "Existing tests for high-dimensional white noise are tailored to the two ends of the sparsity spectrum: maximum-type statistics excel against a few dominant correlations and sum-type statistics against many weak ones, leaving the intermediate regime without a systematic tool. We propose a family of $U$-statistics built from the entry-wise $\\ell_a$-norms of the sample autocovariance matrices, in which the even order $a$ interpolates between the sum-type ($a=2$) and maximum-type ($a\\to\\infty$) endpoints. As $p$ and $T$ diverge jointly, martingale difference theory yields joint asymptotic normality across orders together with asymptotic independence, so that several orders can be combined after a simple calibration. Neither cross-sectional independence nor a mixing condition is required, only a spectral condition on $\\bSig_0$; the derivation links cross-sectional correlation to a graph structure that prices each moment edge by edge. Simulations confirm accurate size and power that is stable across sparse, intermediate and dense alternatives, and show that the low-order members of the family retain their level under conditional heteroscedasticity, where the existing tests distort severely.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04968",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuanya Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hvsjtjd8vyps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04968",
  "fulltext_url": null,
  "id": "6hvsjtjd8vyps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.04968",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7160517743",
  "pdf_url": "https://arxiv.org/pdf/2605.04968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hvsjtjd8vyps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2605.04968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Tests for white noise via asymptotically independent U-statistics in high-dimensions",
  "title_text": "Tests for white noise via asymptotically independent U-statistics in high-dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/6hvsjtjd8vyps",
  "venue": "arXiv",
  "versions": []
}