{
  "abstract": "This paper develops estimator-level asymptotic theory for maximum Diaconis-Ylvisaker prior penalised likelihood for logistic regression with a jointly fitted intercept and nonzero prior slope direction in the proportional-limit regime. For $\\mathrm{N}(\\mathbf{0}_p, p^{-1}\\mathbf{I}_p)$ Gaussian covariates and $p/n\\toκ\\in(0,1)$, a conditional convex Gaussian min--max analysis yields almost-sure convergence of the fitted intercept and a pseudo-Lipschitz empirical law for the slope estimator. This estimator-level law gives asymptotic limits for out-of-sample scores, classification error, optimal thresholding and oracle calibration. It also yields oracle-adjusted fixed-block $Z$-statistics under isotropic Gaussian covariates, and yields the main ingredient in establishing the limiting distribution of the penalised likelihood-ratio test statistic and identifies the rescaling to recover the nominal chi-square distribution. We extend these results to Gaussian designs with arbitrary deterministic mean and positive-definite covariance via affine centering and whitening and discuss extensions to subgaussian covariates. Finally, we propose a consistent response-moment estimator of the oracle parameters entering the state equations that govern the slope limiting law and are required for feasible inference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09831",
  "author_total": 1,
  "authors": [
    {
      "name": "Philipp Sterzinger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7s4x2b40raj46.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09831",
  "fulltext_url": null,
  "id": "7s4x2b40raj46",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09831",
  "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.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7212132594",
  "pdf_url": "https://arxiv.org/pdf/2609.09831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7s4x2b40raj46.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Proportional-limit asymptotics for Diaconis-Ylvisaker-penalised logistic regression with fitted intercept",
  "title_text": "Proportional-limit asymptotics for Diaconis-Ylvisaker-penalised logistic regression with fitted intercept",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:22Z",
  "url": "https://research.draconitic.com/paper/7s4x2b40raj46",
  "venue": "arXiv",
  "versions": []
}