{
  "abstract": "E-values provide a flexible framework for statistical inference, but the universal threshold $1/α$ can be conservative when the null distribution has additional structure. We study how structural restrictions limit the worst-case concentration underlying Markov's inequality, using a nondecreasing density model to constrain tail allocation and an $L$-Lipschitz density model to control local concentration. The nondecreasing model gives the minimax rejection threshold, and the Lipschitz condition yields a sharper closed-form threshold with an $O(L^{-1/2})$ relative improvement over $1/α$. We further show that this threshold is asymptotically sharp as $α\\to0$, in the sense that no uniformly valid threshold can improve on it by a fixed positive $L$-dependent amount. We then incorporate the Lipschitz calibration into multiple testing procedures with FDR control and use the same structural information to construct calibrated conditional e-values for anytime-valid sequential inference. Numerical experiments illustrate the resulting gains in discoveries and the trade-offs of the sequential procedures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11186",
  "author_total": 7,
  "authors": [
    {
      "name": "Jiayi Shen"
    },
    {
      "name": "Houzhen Liu"
    },
    {
      "name": "Qirun Zeng"
    },
    {
      "name": "Manhin Poon"
    },
    {
      "name": "Weiqi Yang"
    },
    {
      "name": "Qixin Zhang"
    },
    {
      "name": "Weiwei Zhuang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65t8d7j7wzqfw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11186",
  "fulltext_url": null,
  "id": "65t8d7j7wzqfw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11186",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods in Clinical Trials"
    ]
  ],
  "openalex": "W7221115315",
  "pdf_url": "https://arxiv.org/pdf/2610.11186",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65t8d7j7wzqfw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:03Z",
      "native_id": "2610.11186",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11186"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Improved E-Value Thresholds with Applications to Multiple and Sequential Testing",
  "title_text": "Improved E-Value Thresholds with Applications to Multiple and Sequential Testing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/65t8d7j7wzqfw",
  "venue": "arXiv",
  "versions": []
}