{
  "abstract": "Many nonparametric tests are based on $U$-statistics that are degenerate under the null hypothesis. We develop Boot-AVT, a bootstrap procedure for asymptotically anytime-valid testing with these statistics. Using Brownian scaling and time inversion for the limiting Gaussian chaos process, we show that logarithmically penalized maxima over observed and future sample sizes have a common limiting null distribution. A quadratic multiplier bootstrap estimates the corresponding critical values. We also develop Boot-AVT-Multi for joint testing with multiple kernels. For both procedures, we establish uniform consistency of the bootstrap critical values, explicit bounds on size distortion, and asymptotic size $α$ over an unbounded monitoring horizon as the monitoring start tends to infinity. Under fixed alternatives, we derive finite-horizon power bounds and establish power one with finite expected stopping times. Simulation studies evaluate finite-sample size and power in goodness-of-fit, two-sample and independence testing, and real-data analyses compare stopping times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28931",
  "author_total": 4,
  "authors": [
    {
      "name": "Jixuan Liu"
    },
    {
      "name": "Long Feng"
    },
    {
      "name": "Liuhua Peng"
    },
    {
      "name": "Zhaojun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06dmagnqzwzjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28931",
  "fulltext_url": null,
  "id": "06dmagnqzwzjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28931",
  "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|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7223242996",
  "pdf_url": "https://arxiv.org/pdf/2610.28931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06dmagnqzwzjw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Boot-AVT: Asymptotically Anytime-Valid Testing with Degenerate U-Statistics via Bootstrap",
  "title_text": "Boot-AVT: Asymptotically Anytime-Valid Testing with Degenerate U-Statistics via Bootstrap",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:29Z",
  "url": "https://research.draconitic.com/paper/06dmagnqzwzjw",
  "venue": "arXiv",
  "versions": []
}