{
  "abstract": "For Gaussian location mixtures with identity covariance, we prove that the nonparametric maximum likelihood estimator of the mixing distribution is unique for Lebesgue-almost every dataset, for every sample size and dimension. In particular, uniqueness holds almost surely whenever the joint distribution of the observations is absolutely continuous. The proof uses the finite-support theorem for Gaussian location NPMLEs and almost-everywhere differentiability of the optimal log-likelihood. Wherever this optimal value is differentiable, all NPMLEs have the same density derivatives at the observations. A minimal linear dependence among Gaussian evaluation vectors then rules out distinct solutions. An appendix extends the result to arbitrary fixed, known, observation-specific positive-definite covariances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23903",
  "author_total": 1,
  "authors": [
    {
      "name": "Haiyang Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aq5wv7rf73xn1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23903",
  "fulltext_url": null,
  "id": "aq5wv7rf73xn1",
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  "landing_url": "https://arxiv.org/abs/2609.23903",
  "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"
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      "arxiv",
      "stat.TH"
    ],
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      "openalex",
      "1702|Bayesian Methods and Mixture Models"
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  "openalex": "W7214030217",
  "pdf_url": "https://arxiv.org/pdf/2609.23903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aq5wv7rf73xn1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Almost-sure uniqueness of the Gaussian location NPMLE",
  "title_text": "Almost-sure uniqueness of the Gaussian location NPMLE",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/aq5wv7rf73xn1",
  "venue": "arXiv",
  "versions": []
}