ArticleAnnals of statistics2010
Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error.
Article in Annals of statistics, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 34 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
34 citing papers in PubMed, 107 citations in OpenAlex.
- Measuring Regulatory Network Inheritance in Dividing Yeast Cells Using Ordinary Differential Equations.bioRxiv : the preprint server for biology · 2025Article
- A biomathematical model of SARS-CoV-2 in Syrian hamsters.Scientific reports · 2024Article
- Specification testing for ordinary differential equation models with fixed design and applications to COVID-19 epidemic models.Computational statistics & data analysis · 2023Article
- A biomathematical model of atherosclerosis in mice.PloS one · 2022Article
- Combining data assimilation and machine learning to build data-driven models for unknown long time dynamics-Applications in cardiovascular modeling.International journal for numerical methods in biomedical engineering · 2021Article
- Integration of single-cell multi-omics for gene regulatory network inference.Computational and structural biotechnology journal · 2020Review
- The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models.Inverse problems · 2019Article
- Modeling Quorum Sensing Dynamics and Interference onFrontiers in microbiology · 2019Article
- Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach.Journal of the American Statistical Association · 2019Article
- Parameter Estimation for Semiparametric Ordinary Differential Equation Models.Communications in statistics: theory and methods · 2019Article
- A Functional Data Method for Causal Dynamic Network Modeling of Task-Related fMRI.Frontiers in neuroscience · 2019Article
- Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks.Statistics in medicine · 2018Article
- Statistical inference in mechanistic models: time warping for improved gradient matching.Computational statistics · 2018Article
- Article
- Network Reconstruction From High-Dimensional Ordinary Differential Equations.Journal of the American Statistical Association · 2017Article
- Statistical analysis of differential equations: introducing probability measures on numerical solutions.Statistics and computing · 2017Article
- Hierarchical effects of pro-inflammatory cytokines on the post-influenza susceptibility to pneumococcal coinfection.Scientific reports · 2016Article
- Controllability and stability analysis of large transcriptomic dynamic systems for host response to influenza infection in human.Infectious Disease Modelling · 2016Article
- Review
- Quantifying Immune Response to Influenza Virus Infection via Multivariate Nonlinear ODE Models with Partially Observed State Variables and Time-Varying Parameters.Statistics in biosciences · 2015Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
3 authors at 1 institution in 1 country.
Funding
Abstract
This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge-Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurement error. The B-spline is used to approximate the time-varying coefficients, and the corresponding asymptotic theories in this case are investigated under the framework of the sieve approach. Our results show that if the maximum step size of the p-order numerical algorithm goes to zero at a rate faster than n(-1/(p∧4)), the numerical error is negligible compared to the measurement error. This result provides a theoretical guidance in selection of the step size for numerical evaluations of ODEs. Moreover, we have shown that the numerical solution-based NLS estimator and the sieve NLS estimator are strongly consistent. The sieve estimator of constant parameters is asymptotically normal with the same asymptotic co-variance as that of the case where the true ODE solution is exactly known, while the estimator of the time-varying parameter has the optimal convergence rate under some regularity conditions. The theoretical results are also developed for the case when the step size of the ODE numerical solver does not go to zero fast enough or the numerical error is comparable to the measurement error. We illustrate our approach with both simulation studies and clinical data on HIV viral dynamics.
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.