{
  "abstract": "This paper studies robust uncertainty quantification for separable nonlinear least squares (SNLLS) problems. We propose two identification methods, (i) Residual-Perturbed Gradient (RPG) and (ii) Global-Fit-Gap (GFG), to construct joint distribution-free confidence regions for both the linear and nonlinear parameters. By exploiting assumed group invariance of the noise (such as symmetry or exchangeability), we apply random perturbations (such as sign-changes or permutations) to build the regions based on resampling and ranking. We prove that both methods guarantee non-asymptotically exact coverage (type I error). Finally, we illustrate the constructions through two numerical experiments: (i) identifying generalized finite impulse response (GFIR) systems using Laguerre polynomials with an adjustable decay rate and (ii) fitting Gaussian radial basis function (RBF) models with variable knots and widths.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39549",
  "author_total": 3,
  "authors": [
    {
      "name": "Szabolcs Szentpéteri"
    },
    {
      "name": "Péter Kovács"
    },
    {
      "name": "Balázs Csanád Csáji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hnmmbn763h0e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39549",
  "fulltext_url": null,
  "id": "8hnmmbn763h0e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39549",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39549",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hnmmbn763h0e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39549",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39549"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Non-Asymptotic Confidence Regions for Separable Nonlinear Models",
  "title_text": "Non-Asymptotic Confidence Regions for Separable Nonlinear Models",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/8hnmmbn763h0e",
  "venue": "arXiv",
  "versions": []
}