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PreprintarXiv licencearXiv

Non-Asymptotic Confidence Regions for Separable Nonlinear Models

  • Szabolcs Szentpéteri
  • Péter Kovács
  • Balázs Csanád Csáji
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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.

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Cite

BibTeXRIS
BibTeX
@misc{szentpeteri2026nonasymptotic,
  title = {{Non-Asymptotic Confidence Regions for Separable Nonlinear Models}},
  author = {Szabolcs Szentpéteri and Péter Kovács and Balázs Csanád Csáji},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39549},
  eprint = {2610.39549},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39549},
}
RIS
TY  - UNPB
TI  - Non-Asymptotic Confidence Regions for Separable Nonlinear Models
AU  - Szabolcs Szentpéteri
AU  - Péter Kovács
AU  - Balázs Csanád Csáji
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39549
UR  - https://arxiv.org/abs/2610.39549
AB  - 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.
ER  -