{
  "abstract": "We present an optimal tester for support size that determines whether an unknown probability distribution is supported on $n$ elements or $\\varepsilon$-far away (in total variation distance) with sample complexity $Θ(\\frac{n}{\\varepsilon\\log(n)})$, improving the prior best $O(\\frac{n}{\\varepsilon\\log(n)} \\log(\\min\\{\\frac{1}{\\varepsilon}, n\\}))$ due to Ferreira Pinto Jr. and Harms (STOC 2025). As a generalization, we provide a pretty good lower bound on support size.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18723",
  "author_total": 1,
  "authors": [
    {
      "name": "Qisheng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/chbjvvve92b17.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18723",
  "fulltext_url": null,
  "id": "chbjvvve92b17",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18723",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
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      "arxiv",
      "cs.IT"
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      "arxiv",
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      "arxiv",
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      "arxiv",
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      "openalex",
      "1703|Complexity and Algorithms in Graphs"
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  "openalex": "W7221764491",
  "pdf_url": "https://arxiv.org/pdf/2610.18723",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/chbjvvve92b17.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18723",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18723"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Support Size Testing",
  "title_text": "Optimal Support Size Testing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/chbjvvve92b17",
  "venue": "arXiv",
  "versions": []
}