{
  "abstract": "We study finite-sample valid tests of the one-sided mean hypothesis $H_0:μ\\leq 1$ against $H_1:μ>1$ for nonnegative random variables. To do so, we develop a leave-one-out dual certificate framework, where certain pointwise inequalities imply p-value validity under the conditional mean null $\\mathbb{E}[X_i\\mid\\mathbf{X}_{-i}]\\leq 1$, and which also gives conditions that allow combining dual certificates for p-values to show that their pointwise minimum is also a valid p-value. The framework proves finite-sample validity of Wang and Zhao's nonparametric likelihood-ratio statistic $T_{\\mathrm{nplr}}$, yields a new p-value $T_{\\mathrm{bin}+}$ extending the Clopper--Pearson binomial test to general nonnegative random variables, and shows that the pointwise minimum $\\min\\{T_{\\mathrm{nplr}},T_{\\mathrm{bin}+}\\}$ is itself a valid and more powerful p-value. We establish sharp optimality results for such testing problems in two regimes: both $T_{\\mathrm{nplr}}$ and $T_{\\mathrm{bin}+}$ attain a universal detectability boundary for the null $H_0$ without moment or tail assumptions, and $T_{\\mathrm{bin}+}$ attains a nonparametric power lower bound under $n^{-1/2}$-local alternatives to $H_0$. Efficient algorithms and numerical experiments demonstrate substantial finite-sample power gains over existing valid methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05360",
  "author_total": 2,
  "authors": [
    {
      "name": "Yifan Zhu"
    },
    {
      "name": "John C. Duchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27q1ksyfhc8bm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05360",
  "fulltext_url": null,
  "id": "27q1ksyfhc8bm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05360",
  "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.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.05360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27q1ksyfhc8bm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05360"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Finite-sample nonparametric mean tests: Leave-one-out duality and asymptotic optimality",
  "title_text": "Finite-sample nonparametric mean tests: Leave-one-out duality and asymptotic optimality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:25Z",
  "url": "https://research.draconitic.com/paper/27q1ksyfhc8bm",
  "venue": "arXiv",
  "versions": []
}