{
  "abstract": "We study randomized multiple testing with e-values under arbitrary dependence and introduce a conditional certification constraint: Given the observed evidence, each coordinate's expected rejection certificate must not exceed its e-value. Existing randomized e-BH improvements satisfy this constraint but have no established optimality guarantee. We prove that the maximum conditional inclusion probability for hypothesis $i$, given e-values~$x$, is $1 \\wedge (α/ K) \\sum_j \\min(x_i, x_j)$, and construct one rule attaining these bounds simultaneously. The rule uses a single independent uniform variable, rejects a prefix of the ordered e-values, and has a unique conditional rejection-set law among rules attaining all the bounds. It therefore maximizes every nonnegative weighted sum of inclusion probabilities, including expected true discoveries under any truth configuration. Under a shared uniform draw, its rejection set contains those of e-BH and U-eBH. The construction extends to BY-calibrated p-values, and simulations under positive and negative dependence show power gains over existing randomized procedures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01333",
  "author_total": 2,
  "authors": [
    {
      "name": "Soumyabrata Bose"
    },
    {
      "name": "Jay Bartroff"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ena64m3cfp86.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01333",
  "fulltext_url": null,
  "id": "7ena64m3cfp86",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01333",
  "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/2611.01333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ena64m3cfp86.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01333"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Certified Multiple Testing with E-values",
  "title_text": "Optimal Certified Multiple Testing with E-values",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/7ena64m3cfp86",
  "venue": "arXiv",
  "versions": []
}