{
  "abstract": "Classical preliminary-test and Stein-type estimators interpolate between restricted and full regression fits, but OLS and chi-squared calibration fail when $p\\gg n$ and the restriction is data-adaptive. We propose an honest sample-separated framework built around a common selected-null law. Independent selection data extend a mandatory core; separate estimation data pair a complete-design regularized full-model (FM) fit with a fresh exact-null submodel refit. A maximum residual-association statistic assesses all excluded coordinates. Projected Gaussian draws reproduce its conditional null distribution under homoskedastic Gaussian errors, yielding a finite-sample-valid rank test. The inverse moment of the same design-specific law replaces $q-2$ and calibrates preliminary-test (PT), Stein-type (S), and positive-part Stein-type (PS) rules. We derive exact endpoint-risk formulas, honest conditional validity, null-law concentration, inverse-moment consistency, an explicit selection-failure remainder, and endpoint adaptivity without uniform-dominance claims. Gaussian experiments with 2,000 replications and up to 30,000 predictors compare Ridge and LASSO FMs, tuned by frozen-fold cross-validation, under a common submodel, test, and calibration. PS provides large near-null coefficient-risk gains and approaches the relevant full-model risk under strong departures. A separate CPSS-LASSO/CPSS-MCP audit evaluates data-adaptive selection, while a split-sample DepMap study with 19,152 predictors illustrates prediction gains and sensitivity to error assumptions. The HDMaxShrink R package implements the procedure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23070",
  "author_total": 1,
  "authors": [
    {
      "name": "Bahadır Yüzbaşı"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/feq71ma0q1qw0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23070",
  "fulltext_url": null,
  "id": "feq71ma0q1qw0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23070",
  "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 Methods and Inference"
    ]
  ],
  "openalex": "W7214011640",
  "pdf_url": "https://arxiv.org/pdf/2609.23070",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/feq71ma0q1qw0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:33Z",
      "native_id": "2609.23070",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23070"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Max-Test-Calibrated Stein Shrinkage with Honest Submodel Selection in Ultra-High-Dimensional Regression",
  "title_text": "Max-Test-Calibrated Stein Shrinkage with Honest Submodel Selection in Ultra-High-Dimensional Regression",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/feq71ma0q1qw0",
  "venue": "arXiv",
  "versions": []
}