{
  "abstract": "We study L-PASSO, a penalized least-squares regression method based on the logarithmic penalty $λ\\sum_j\\log(1+|β_j|/τ)$, and its two-stage adaptive form, in which the scales $τ_j$ come from a pilot estimator. Although this concave penalty has been proposed previously, its variable-selection properties and sparsity relative to other popular penalties have not been fully characterized. We derive the exact orthogonal-design solution, and show that the single-stage estimator selects the true model under a weighted irrepresentable condition that holds for every design once $τ$ is small. We further establish that, under matched tuning, the two-stage estimator possesses the oracle property and has half the asymptotic bias of the adaptive LASSO. Our main theoretical contribution concerns the robustness of the two-stage procedure to the pilot estimator. We show that two-stage L-PASSO remains selection consistent even when the weights associated with relevant variables are as small as $\\exp\\{-o(1/ζ_n)\\}$, whereas the adaptive LASSO fails to retain relevant variables whose pilot weights are sufficiently small relative to its tuning parameter $ζ_n$. We establish that both thresholds are sharp. In high-dimensional settings, we prove support recovery for a local minimizer without imposing any lower-bound condition on the weights of relevant variables, and provide conditions under which this local minimizer is also the unique global minimizer. We additionally establish the selection consistency of a BIC-based tuning-parameter selection procedure. Finally, simulations comparing L-PASSO with the LASSO, SCAD, MCP, SELO, uniLasso, and the adaptive LASSO show that L-PASSO most frequently recovers the true support. Two real-data examples further illustrate the method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38092",
  "author_total": 3,
  "authors": [
    {
      "name": "Samiran Ghosh"
    },
    {
      "name": "Shuva Gupta"
    },
    {
      "name": "Shreyo Ghosh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dccm0hvyq64ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38092",
  "fulltext_url": null,
  "id": "dccm0hvyq64ca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38092",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38092",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dccm0hvyq64ca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2610.38092",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38092"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "L-PASSO: Adaptive Log-penalized Variable Selector, with Sparse Selection and Robustness to the Pilot Estimator",
  "title_text": "L-PASSO: Adaptive Log-penalized Variable Selector, with Sparse Selection and Robustness to the Pilot Estimator",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/dccm0hvyq64ca",
  "venue": "arXiv",
  "versions": []
}