{
  "abstract": "Asymptotic independence between sum-type and maximum-type statistics arises repeatedly across many areas of probability and statistics, particularly in high-dimensional testing and random matrix theory. Motivated by the shared structure underlying existing proofs, which is obscured by their model-specific formulations, this note isolates a common intermediate principle. We introduce a finite-exceedance dependence principle: if the finite-exceedance dependence error vanishes at every fixed order and high-order exceedances are mildly controlled, then a finite-order Bonferroni argument yields asymptotic independence between the sum and the maximum. We further give an independent-proxy criterion for verifying this: for each finite set of exceedances, it suffices to construct an exactly independent proxy for the sum-type statistic whose approximation error is negligible in aggregate. Local deletion under dependency graphs and Gaussian regression and residualization are two examples. The framework gives modular derivations of existing sum--max independence results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03351",
  "author_total": 1,
  "authors": [
    {
      "name": "Hongjian Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dn46g7zhys150.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03351",
  "fulltext_url": null,
  "id": "dn46g7zhys150",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03351",
  "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.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dn46g7zhys150.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A Note on the Finite-Exceedance Dependence Principle for Sum--Maximum Asymptotic Independence",
  "title_text": "A Note on the Finite-Exceedance Dependence Principle for Sum--Maximum Asymptotic Independence",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/dn46g7zhys150",
  "venue": "arXiv",
  "versions": []
}