{
  "abstract": "Density deconvolution is an ill-posed inverse problem because recovering the latent density amplifies high-frequency variation in the observed data. We propose a two-stage likelihood procedure. The first estimator maximizes the convolution likelihood over a regularized Gaussian-mixture sieve; the second treats this fit as an empirical prior and averages the fitted conditional latent densities. Under fixed-model misspecification, the estimators generally have different population targets. For bounded local multiplicative perturbations of the latent density, the population posterior map is locally contractive in chi-square divergence under identifiable convolution. Under correct finite-dimensional specification, however, reconstruction adds a nonnegative first-order variance component. For growing sieves, we separate observed-domain estimation, inverse stability, and posterior empirical variation. We derive explicit rates under Gaussian error and recover the classical ordinary-smooth exponent, up to logarithmic factors, with a constructive verification for Laplace error. Simulations and a Framingham blood-pressure application provide empirical performance evidences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.00240",
  "author_total": 4,
  "authors": [
    {
      "name": "Marco Di Marzio"
    },
    {
      "name": "Stefania Fensore"
    },
    {
      "name": "Chiara Passamonti"
    },
    {
      "name": "Serena Pulcini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0e8py6t6q44sa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.00240",
  "fulltext_url": null,
  "id": "0e8py6t6q44sa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.00240",
  "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.TH"
    ],
    [
      "openalex",
      "1702|Bayesian Methods and Mixture Models"
    ]
  ],
  "openalex": "W7172445457",
  "pdf_url": "https://arxiv.org/pdf/2608.00240",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0e8py6t6q44sa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.00240",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.00240"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Regularized-Likelihood Deconvolution with Posterior-Density Reconstruction",
  "title_text": "Regularized-Likelihood Deconvolution with Posterior-Density Reconstruction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/0e8py6t6q44sa",
  "venue": "arXiv",
  "versions": []
}