{
  "abstract": "This paper establishes a unified non-linear regularization framework for high-dimensional $M$-estimation, encompassing both linear regression and Cox's proportional hazards models. Rather than relying on traditional additive non-convex penalties, the proposed paradigm embeds sparsity directly into the parameter mapping using a smooth ($C^2$) component-wise ReParametrization map for Sparsity (RePS). This geometric formulation dynamically adapts to local parameter scales, successfully suppressing high-dimensional noise and recovering unbiased oracle asymptotic normality under the large-sample limit. Through the Primal-Dual Witness method, we establish a unified oracle equivalence for both model classes under a liberated micro-penalty scaling regime $λ\\ll n^{-1/2}$, effectively accommodating model-specific structures such as the shift-invariance in survival analysis. Extensive Monte Carlo simulations demonstrate that the RePS framework consistently achieves near-perfect false-positive control and optimal 95\\% confidence interval coverage, outperforming conventional non-convex regularizers (SCAD and MCP) which suffer from severe variance inflation and under-coverage due to post-selection noise leakage.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19558",
  "author_total": 1,
  "authors": [
    {
      "name": "Yoichi Nishiyama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brfh7agbv1qs5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19558",
  "fulltext_url": null,
  "id": "brfh7agbv1qs5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19558",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7213596032",
  "pdf_url": "https://arxiv.org/pdf/2609.19558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brfh7agbv1qs5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2609.19558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Oracle high-dimensional $M$-estimation using smooth reparameterization for sparsity",
  "title_text": "Oracle high-dimensional M-estimation using smooth reparameterization for sparsity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:13Z",
  "url": "https://research.draconitic.com/paper/brfh7agbv1qs5",
  "venue": "arXiv",
  "versions": []
}