{
  "abstract": "When a parameter is bounded, the likelihood ratio statistic does not generally follow the chi-square limit distribution of Wilks' theorem. In fact, its asymptotic null distribution depends on the distance from the null value to the boundary, interpolating between the chi-bar-square law on the boundary and the chi-square law in the deep interior of the parameter space. We derive this distribution and use it to construct confidence curves, which are nested collections of two-sided confidence intervals or regions, for bounded parameters. We extend the existing result for the scalar parameter to a two-dimensional parameter with one or both components bounded. As the bivariate distributions are integrals of normal distributions, which are not reducible to standard statistical functions, we also give a simpler approximated distribution obtained by moment-matching. We illustrate the methods on a canonical analysis from high-energy physics, namely the Poisson signal-plus-background experiment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28235",
  "author_total": 4,
  "authors": [
    {
      "name": "Hedvig Borgen Reiersrud"
    },
    {
      "name": "Clara Bertinelli Salucci"
    },
    {
      "name": "Riccardo De Bin"
    },
    {
      "name": "Alessandra Rosalba Brazzale"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1abys8y7qdxv6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28235",
  "fulltext_url": null,
  "id": "1abys8y7qdxv6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28235",
  "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",
      "hep-ex"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7223104105",
  "pdf_url": "https://arxiv.org/pdf/2610.28235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1abys8y7qdxv6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28235"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    }
  ],
  "title": "Likelihood-Based Confidence Curves for Bounded Parameters",
  "title_text": "Likelihood-Based Confidence Curves for Bounded Parameters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:13Z",
  "url": "https://research.draconitic.com/paper/1abys8y7qdxv6",
  "venue": "arXiv",
  "versions": []
}