{
  "abstract": "The Oracle Approximating Shrinkage (OAS) estimator provides a closed-form, data-driven shrinkage intensity for regularizing sample covariance matrices toward a scaled identity target, but its derivation assumes Gaussian data. In practice, financial returns, neural signals, and many other high-dimensional datasets exhibit heavy tails and non-zero kurtosis, violating this assumption. We extend OAS to any distribution with finite fourth moments by incorporating a correction term $α$ built from the fourth-order joint cumulants of the data. The correction vanishes under Gaussianity, recovering the OAS formula as a special case; it admits a consistent $O(np)$ sample estimator and satisfies $ρ\\in [0, 1]$ exactly for both the population cumulant and its sample analogue. Simulations and an equity-returns study confirm that the correction closes the gap between OAS and the Ledoit-Wolf estimator under non-Gaussian data, with OAS-Extended performing comparably across all tested settings. The contribution is a principled correction for OAS practitioners facing heavy-tailed data; structurally, it is distinct from prior work extending Ledoit-Wolf to elliptical distributions, which optimizes against a fixed oracle target and yields a different closed-form formula.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22144",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael J. Lewis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2f21d1fr0taew.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22144",
  "fulltext_url": null,
  "id": "2f21d1fr0taew",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22144",
  "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",
      "q-fin.MF"
    ],
    [
      "arxiv",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.22144",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2f21d1fr0taew.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:00Z",
      "native_id": "2610.22144",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22144"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Extending the Oracle Approximating Shrinkage to General Distributions",
  "title_text": "Extending the Oracle Approximating Shrinkage to General Distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/2f21d1fr0taew",
  "venue": "arXiv",
  "versions": []
}