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  "title": "Unlinked Gamma regression: exact identifiability and optimal cumulant order",
  "shortTitle": "Lost links, finite choices",
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  "oneLine": "A minimal counterexample, a complete coefficient-fiber classification, and the exact condition that restores identification.",
  "abstract": "When predictor and response observations lose their links, even independent non-Gaussian predictors can admit distinct minimal coefficient vectors. This unrefereed candidate classifies every ambiguity for a fixed known Gamma shape dictionary, gives a sharp subset-sum condition for identification, and proves an optimal worst-case consecutive cumulant cutoff. It is a population theorem, not a validated finite-sample estimator.",
  "datePublished": "2026-09-20",
  "dateModified": "2026-09-20",
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  "doi": "10.5281/zenodo.22858495",
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    {
      "citation": "Balabdaoui, Slawski and Steffani (2025), Identifiability in unlinked linear regression, version 1. Targeted conjecture and Gamma convolution obstacle.",
      "url": "https://arxiv.org/abs/2507.14986v1",
      "doi": "10.48550/arXiv.2507.14986"
    },
    {
      "citation": "Azadkia and Balabdaoui (2024), Linear regression with unmatched data: A deconvolution perspective. Statistical estimation context.",
      "url": "https://jmlr.org/papers/v25/22-0930.html",
      "doi": null
    },
    {
      "citation": "Balabdaoui, Di Noia and Durot (2026), Deconvolution in unlinked linear models. Latent-law estimation with nonunique coefficients.",
      "url": "https://jmlr.org/papers/v27/25-0516.html",
      "doi": null
    },
    {
      "citation": "James, Roynette and Yor (2008), Generalized Gamma convolutions, Dirichlet means, Thorin measures, with explicit examples. Classical invariant context.",
      "url": "https://doi.org/10.1214/07-PS118",
      "doi": "10.1214/07-PS118"
    },
    {
      "citation": "Kunis, Peter, Römer and von der Ohe (2016), A multivariate generalization of Prony’s method. Classical reconstruction machinery.",
      "url": "https://doi.org/10.1016/j.laa.2015.10.023",
      "doi": "10.1016/j.laa.2015.10.023"
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