{
  "abstract": "Statistical precision and scientific relevance operate on different scales. In regular problems, sampling uncertainty contracts at rate $n^{-1/2}$, whereas the magnitude below which an effect is scientifically negligible may be fixed or may vary with information. Let $Δ_n$ denote a relevance threshold and $I_0$ Fisher information, and define $λ_n=\\sqrt{nI_0}Δ_n$. For separated negligible and meaningful parameter classes, we establish the minimax lower bound $\\liminf R_n^*\\ge 2\\{1-Φ(\\varepsilonκ)\\}$ when $λ_n\\toκ$. If $λ_n\\to0$, the experiments merge and consistent classification is impossible. If $λ_n\\toκ\\in(0,\\infty)$, the problem converges to a Gaussian-shift decision problem. We characterize the exact minimax rule and risk in that limiting composite problem. As $κ\\downarrow0$, the optimal cutoff converges to one statistical-error unit and the optimal improvement over trivial risk is $O(κ^2)$, while a simple relevance-boundary rule improves only at $O(κ^3)$; as $κ$ grows, that rule becomes asymptotically minimax. If $λ_n\\to\\infty$, consistent classification is attainable under a uniform estimation-resolution condition, verified for Gaussian and Bernoulli models. For $Δ_n=dn^{-γ}$, the critical rate is $γ=1/2$. We also show that moving asymmetric relevance regions depend on standardized distances to their two boundaries rather than total width alone. For heterogeneous true effects, we derive a significance-saturation limit and show that point-null significance can be most selective for scientifically relevant effects at intermediate information. The framework characterizes when scientific relevance is statistically resolvable through a common information scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15811",
  "author_total": 1,
  "authors": [
    {
      "name": "Subir Hait"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1h2g8xazkvja8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15811",
  "fulltext_url": null,
  "id": "1h2g8xazkvja8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15811",
  "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",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7213247111",
  "pdf_url": "https://arxiv.org/pdf/2609.15811",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1h2g8xazkvja8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.15811",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15811"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "When Is a Relevance Threshold Statistically Resolvable? Minimax Limits for Effect Classification",
  "title_text": "When Is a Relevance Threshold Statistically Resolvable? Minimax Limits for Effect Classification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:51Z",
  "url": "https://research.draconitic.com/paper/1h2g8xazkvja8",
  "venue": "arXiv",
  "versions": []
}