{
  "abstract": "In this paper, we establish refined Cramér-type moderate deviations for dependent random variables at any fixed order $m\\geq3$. Combining higher-order Stein identities with exponential tilting, we obtain cumulant-corrected tail approximations with explicit error bounds for boundedly supported kernels. Our main application gives a fourth-order expansion under bounded local dependence, reaching an $O(n^{3/10})$ deviation range under standard normalization with fixed dependence parameters. It improves on previous work in both deviation range and applicability, and also covers bounded $m$-dependent sequences without an independent-base representation. Further applications to the generalized combinatorial central limit theorem and the Curie-Weiss model also extend some earlier results under permutation and mean-field dependence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29078",
  "author_total": 3,
  "authors": [
    {
      "name": "Hui-Lin Liu"
    },
    {
      "name": "Song-Hao Liu"
    },
    {
      "name": "Dawei Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmwftvwzb8g34.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29078",
  "fulltext_url": null,
  "id": "dmwftvwzb8g34",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29078",
  "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",
      "math.PR"
    ],
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      "openalex",
      "2613|Probability and Statistical Research"
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  ],
  "openalex": "W7223203582",
  "pdf_url": "https://arxiv.org/pdf/2610.29078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmwftvwzb8g34.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Refined Cramér-type moderate deviations by Stein's method under dependence",
  "title_text": "Refined Cramér-type moderate deviations by Stein's method under dependence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/dmwftvwzb8g34",
  "venue": "arXiv",
  "versions": []
}