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Nonparametric Estimation under General Nonlinear ODE Constraints: A Comparison with Parametric ODE-Fitting Methods — arXiv:2608.05081

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.05081
License (as archived): CC0-1.0
Archived: 2026-10-31T11:37:30.903Z
SHA-256 of the archived text: 7ce54c15608b555898304a90ba76bf991384a2861c189fa57ded333ce3625e7a
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How to cite

Nonparametric Estimation under General Nonlinear ODE Constraints: A Comparison with Parametric ODE-Fitting Methods — arXiv:2608.05081 — arXiv (en), https://arxiv.org/abs/2608.05081 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cf159a2ecfee (Metraipolis archive dc_cf159a2ecfee, sha256 7ce54c15608b555898304a90ba76bf991384a2861c189fa57ded333ce3625e7a)

BibTeX

@misc{dccf159a2ecfee,
  title = {Nonparametric Estimation under General Nonlinear ODE Constraints: A Comparison with Parametric ODE-Fitting Methods — arXiv:2608.05081},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.05081},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cf159a2ecfee; sha256 7ce54c15608b555898304a90ba76bf991384a2861c189fa57ded333ce3625e7a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.05081. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Many physical, biological, and epidemiological processes are governed by ordinary differential equations (ODEs) that are nonlinear in the state variable, including logistic population growth, chemical reaction kinetics, and epidemiological compartment models. We develop a differential equation-constrained local polynomial regression (DE-constrained LPR) framework for the general first-order ODE constraint g'(x) = F(x, g(x)), where F may be any Lipschitz continuous function, extending prior work restricted to exponential and linear ODE structures. Because F is generally nonlinear in g, the Taylor coefficients of the DE1-k estimator cannot be written in closed form; instead they are obtained by successive symbolic differentiation of F, and the estimator is computed by nonlinear least squares, requiring only a single local parameter at each evaluation point regardless of polynomial degree k. We derive the asymptotic conditional bias and variance of the DE1-k estimator, propose an AIMSE-optimal bandwidth that exploits the ODE structure to avoid direct estimation of high-order derivatives, and evaluate the method in a simulation study based on logistic growth, benchmarking against the parameter cascading method of Ramsay et al. (2007) (PCODE) and classical local linear regression. The DE-constrained estimator consistently outperforms local linear regression and is competitive with PCODE even though it estimates no structural parameter of the ODE; a sensitivity analysis across growth rates shows DE-constrained estimation becomes more accurate and more robust than PCODE as the curve steepens and PCODE's parameter estimation grows less stable. These results position DE-constrained LPR as a practical nonparametric alternative to parametric ODE-fitting methods when structural parameters are difficult to identify reliably.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-06 in stat.ME).
Categorie arXiv: Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2608.05081 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-31T11:27:30.244Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-08-06?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).