{
  "abstract": "Blest's rank correlation $ν$ is a variant of Spearman's rho $ρ$ that weights the leading ranks of one variable more heavily, at the price that $ν$ is not symmetric in its arguments. We quantify both features by determining the exact region of $(ρ,ν)$ over all bivariate copulas, as well as that of $(η,ν)$, where $η$ is the symmetrized Blest coefficient of Genest and Plante. The latter region is a linear image of the set of all pairs $(ν(C),ν(C^\\top))$ formed by a copula $C$ and its transpose. Consequently, Blest's coefficient differs from Spearman's rho by at most $1/4$, and interchanging the two variables changes it by at most $27/64$, improving on the bound $1/2$ implied by the first inequality. For every given value of $ρ$ or $η$, each corresponding extreme value of $ν$ is attained by exactly one copula, given in closed form and supported on finitely many line segments. Near countermonotonicity, the upper extremizers of the $(η,ν)$-region are supported on the graph of a function of the second coordinate, yet their conditional laws given the first coordinate carry two atoms. The proofs rest on a rearrangement inequality with equality case and on explicit Kantorovich potentials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27634",
  "author_total": 1,
  "authors": [
    {
      "name": "Marcus Rockel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82ycrk5d1jj88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27634",
  "fulltext_url": null,
  "id": "82ycrk5d1jj88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27634",
  "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"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2003|Financial Risk and Volatility Modeling"
    ]
  ],
  "openalex": "W7214196894",
  "pdf_url": "https://arxiv.org/pdf/2609.27634",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82ycrk5d1jj88.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27634",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27634"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Rank weighting and asymmetry in Blest's rank correlation: two exact regions",
  "title_text": "Rank weighting and asymmetry in Blest's rank correlation: two exact regions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/82ycrk5d1jj88",
  "venue": "arXiv",
  "versions": []
}