{
  "abstract": "Statistical modeling of heavy-tailed data with bounded or finite body behaviour often relies on composite or spliced distributions characterized by structural thresholds. Because the probability density function features a sharp directional shift (a cusp) at the join point, the classical log-likelihood function exhibits a discontinuity in its first derivative, causing standard Cramér-Rao regularity conditions and maximum likelihood frameworks to break down. To overcome this non-regularity, we develop a robust, log-transformed asymmetric Huber M-estimation framework for the structural threshold, coupled with conditional shape maximum likelihood estimators. We derive a closed-form parameter-balancing condition that analytically guarantees Fisher consistency under structural tail asymmetry. Furthermore, we establish the joint asymptotic normality of the hybrid Maximum Likelihood and M-estimator system and derive its explicit sandwich covariance structure. A computationally efficient profiled Z-estimation algorithm is implemented to reduce the joint estimation to a one-dimensional root-finding problem. Finite-sample properties are validated through Monte Carlo simulations, and the practical utility of the framework is demonstrated on the benchmark Danish Fire Insurance claims dataset.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30624",
  "author_total": 1,
  "authors": [
    {
      "name": "N Balakrishna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bygp93pvz4hyq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30624",
  "fulltext_url": null,
  "id": "bygp93pvz4hyq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30624",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7223380999",
  "pdf_url": "https://arxiv.org/pdf/2610.30624",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bygp93pvz4hyq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:43Z",
      "native_id": "2610.30624",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30624"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Robust M-Estimation for Spliced Power-Law Models Under Cusp-Type Non-Regularity",
  "title_text": "Robust M-Estimation for Spliced Power-Law Models Under Cusp-Type Non-Regularity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:43Z",
  "url": "https://research.draconitic.com/paper/bygp93pvz4hyq",
  "venue": "arXiv",
  "versions": []
}