{
  "abstract": "This paper studies the finite-sample bias of plug-in estimators for joint entropy, conditional entropy, and mutual information for finitely supported discrete random variables. Using the univariate reduction framework developed in our companion works, we derive explicit first-order bias formulas. For a pair (X,Y) with support sizes r and s, the biases are respectively -(rs-1)/(2n), -r(s-1)/(2n), and (r-1)(s-1)/(2n). We then propose bias-corrected estimators for the three measures and prove that the uncorrected and corrected versions are asymptotically equivalent, differing by a deterministic term of order O(1/n); consequently, they share the same asymptotic distribution. A simulation study validates the theoretical results, including a dedicated independence study and the relationship with Wilks' theorem. An application to a motor insurance portfolio, where X is the driver's age class and Y the claim severity class, illustrates the improvement brought by the bias correction for risk classification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02558",
  "author_total": 1,
  "authors": [
    {
      "name": "Amadou Diadie Ba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fnavjq6px5dd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02558",
  "fulltext_url": null,
  "id": "8fnavjq6px5dd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02558",
  "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.TH"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7220457294",
  "pdf_url": "https://arxiv.org/pdf/2610.02558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fnavjq6px5dd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Bias-Corrected Estimators for Joint Entropy, Conditional Entropy, and Mutual Information in the Discrete Bivariate Case: Theory and an Application to Motor Insurance",
  "title_text": "Bias-Corrected Estimators for Joint Entropy, Conditional Entropy, and Mutual Information in the Discrete Bivariate Case: Theory and an Application to Motor Insurance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:56Z",
  "url": "https://research.draconitic.com/paper/8fnavjq6px5dd",
  "venue": "arXiv",
  "versions": []
}