{
  "abstract": "When testing a composite null $\\mathcal{P}$ against a composite alternative $\\mathcal{Q}$, it has been known since Huber and Strassen (1973) that if a least favorable distribution (LFD) pair exists, then a version of its likelihood ratio yields a minimax optimal test, and Huber (1965) derived a similar result in the sequential setting for a specific robust testing problem that is the focus of the current paper; the same likelihood ratio is log-optimal in the worst case; its expected logarithm under the alternative equals $\\inf_{P \\in \\mathcal{P},S \\in \\mathcal{Q}} KL(S\\|P)$, whose inverse also determines the stopping time of the test under the alternative. These results focus on optimizing worst-case performance, but the resulting methods have lower power if the data come from simpler alternatives. This paper studies an arguably more practical goal of achieving asymptotic \\emph{instance optimality} for ``power-one'' sequential tests, which remarkably may even be possible when $\\mathcal{Q} = \\mathcal{P}^c$. This means that when the data are drawn from any $S \\in \\mathcal{P}^c$, the test has power one, and its stopping time is determined by the larger information number $\\inf_{P \\in \\mathcal{P}} KL(S\\|P)$, which governs the performance of an oracle that knows $S$. To demonstrate this point, our paper focuses on the case of testing a TV ball around a discrete distribution with $d$ components, and designs a computationally and memory efficient algorithm that is also asymptotically instance-optimal. Specifically, we consider two different asymptotic settings: one is the \"Wald setting\", where the type-1 error level $α$ approaches zero for a fixed alternative $S$ and the second is the \"Farrell setting\", where $α$ is fixed and $\\inf_{P \\in \\mathcal{P}} KL(S\\|P)$ approaches $0$. Our sequential test is simultaneously optimal in both regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02130",
  "author_total": 2,
  "authors": [
    {
      "name": "Aytijhya Saha"
    },
    {
      "name": "Aaditya Ramdas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cztpgbafyfps2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02130",
  "fulltext_url": null,
  "id": "cztpgbafyfps2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02130",
  "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.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02130",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cztpgbafyfps2.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02130",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02130"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Beyond least-favorable distribution pairs: asymptotically instance-optimal robust hypothesis testing",
  "title_text": "Beyond least-favorable distribution pairs: asymptotically instance-optimal robust hypothesis testing",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:15Z",
  "url": "https://research.draconitic.com/paper/cztpgbafyfps2",
  "venue": "arXiv",
  "versions": []
}