{
  "abstract": "We give a necessary and sufficient condition for the existence of power-one sequential tests in an i.i.d. composite testing problem. A level-\\(α\\) test with power one against every alternative exists if and only if the alternatives are separated from the null by a countable family of finite-block events. We provide other equivalent conditions using randomized fixed-sample tests, bounded finite-block scores, e-processes, reduced-filtration test supermartingales, and a countable cover whose finite-block weak-$*$ closed convex hulls are positively separated in total variation. As a bonus, the constructive proof yields tests have pointwise expected sample size \\(O_Q(\\log(1/α))\\). Exactly the same conditions also characterize i.i.d.\\ change detectability under optional-horizon average-run-length control: for every \\(η>0\\), they are equivalent to an alarm family \\((T_γ)_{γ\\ge1}\\) satisfying \\(\\Prob_{P^\\infty}(T_γ\\leσ)\\le \\E_{P^\\infty}σ/γ\\) for every null law and every stopping time \\(σ\\). In fact, when these conditions hold, we can construct a single e-detector such that every null-law average run length lies between \\(γ\\) and \\((1+η)γ+1\\), and having robust Lorden delay \\(O_Q(\\logγ)\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05752",
  "author_total": 1,
  "authors": [
    {
      "name": "Aaditya Ramdas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wqqzm8wbg69h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05752",
  "fulltext_url": null,
  "id": "2wqqzm8wbg69h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05752",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7212074999",
  "pdf_url": "https://arxiv.org/pdf/2609.05752",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wqqzm8wbg69h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05752",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05752"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A complete characterization of sequential testability and change detectability in i.i.d. models",
  "title_text": "A complete characterization of sequential testability and change detectability in i.i.d. models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/2wqqzm8wbg69h",
  "venue": "arXiv",
  "versions": []
}