Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error

DOI10.1214/09-AOS784zbMath1203.62049arXiv1010.4162WikidataQ41341797 ScholiaQ41341797MaRDI QIDQ988009

Hongqi Xue, Hongyu Miao, Hulin Wu

Publication date: 24 August 2010

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4162

zbMATH Keywords

ordinary differential equationnonlinear least squarestime-varying parameterRunge-Kutta algorithmspline smoothingsieve approach

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Point estimation (62F10) System identification (93B30) Nonlinear ordinary differential equations and systems (34A34) Generalized stochastic processes (60G20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items

Nonparametric estimation of isotropic covariance function, Laplace based approximate posterior inference for differential equation models, Parameter estimation and inference in dynamic systems described by linear partial differential equations, Two-step Bayesian methods for generalized regression driven by partial differential equations, Robust estimation of constant and time-varying parameters in nonlinear ordinary differential equation models, Bayesian Analysis of ODEs: Solver Optimal Accuracy and Bayes Factors, Identifiability analysis of linear ordinary differential equation systems with a single trajectory, Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research, Optimal Control and Additive Perturbations Help in Estimating Ill-Posed and Uncertain Dynamical Systems, APIK: Active Physics-Informed Kriging Model with Partial Differential Equations, Bayesian inference for higher-order ordinary differential equation models, Parameter estimation for semiparametric ordinary differential equation models, Inference for differential equation models using relaxation via dynamical systems, Bayesian estimation of time-varying parameters in ordinary differential equation models with noisy time-varying covariates, Robust estimation of parameters in nonlinear ordinary differential equation models, Estimation of nonlinear differential equation model for glucose-insulin dynamics in type I diabetic patients using generalized smoothing, Estimating Varying Coefficients for Partial Differential Equation Models, A regularization method for the parameter estimation problem in ordinary differential equations via discrete optimal control theory, Bayesian smooth‐and‐match inference for ordinary differential equations models linear in the parameters, Statistical inference for dynamical systems: a review, Model Checking for Parametric Ordinary Differential Equations Systems, Specification testing for ordinary differential equation models with fixed design and applications to COVID-19 epidemic models, Sieve M-estimator for a semi-functional linear model, Bayesian two-step estimation in differential equation models, Statistical analysis of differential equations: introducing probability measures on numerical solutions, \(\sqrt{n}\)-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing, Time-varying coefficient estimation in differential equation models with noisy time-varying covariates, A refined parameter estimating approach for HIV dynamic model, The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models, Statistical inference in mechanistic models: time warping for improved gradient matching, Time-course window estimator for ordinary differential equations linear in the parameters, Optimal rate of direct estimators in systems of ordinary differential equations linear in functions of the parameters, Numerical discretization-based kernel type estimation methods for ordinary differential equation models, Bayesian inference of a directional brain network model for intracranial EEG data, Inference in dynamic systems using B-splines and quasilinearized ODE penalties, A model-based initial guess for estimating parameters in systems of ordinary differential equations, Parametric Estimation of Ordinary Differential Equations With Orthogonality Conditions, Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling, Generalized Ordinary Differential Equation Models, Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach, Identification of nonparametric monotonic regression models with continuous nonclassical measurement errors, Estimation of Ordinary Differential Equation Models with Discretization Error Quantification

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two likelihood-based semiparametric estimation methods for panel count data with covariates
• Parameter identifiability and estimation of HIV/AIDS dynamic models
• Additive regression and other nonparametric models
• On asymptotically efficient estimation in semiparametric models
• Identifiability results on some constrained compartmental systems
• Asymptotic theory of nonlinear least squares estimation
• Structural identifiability of the parameters of a nonlinear batch reactor model
• Discussion of parameter estimation in biological modelling: Algorithms for estimation and evaluation of the estimates
• System identifiability based on the power series expansion of the solution
• A practical guide to splines
• On global identifiability for arbitrary model parametrizations
• Convergence rate of sieve estimates
• Positive feedback and angiogenesis in tumor growth control
• Ponding problem of plates in nonlinear nature
• Differential evolution -- a simple and efficient heuristic for global optimization over continuous spaces
• On methods of sieves and penalization
• Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity
• Estimation of HIV/AIDS parameters.
• Local asymptotics for polynomial spline regression
• Efficient estimation of the partly linear additive Cox model
• Efficient estimation for the proportional hazards model with interval censoring
• Optimal global rates of convergence for nonparametric regression
• Weak convergence and empirical processes. With applications to statistics
• Parameter estimation of ODE's via nonparametric estimators
• Analysis of the growth of tumor cell populations
• Modeling and estimation of kinetic parameters and replicative fitness of HIV-1 from flow-cytometry-based growth competition experiments
• Robust semiparametric M-estimation and the weighted bootstrap
• Estimation of parameters in incomplete data models defined by dynamical systems
• Estimation and Inference for a Spline-Enhanced Population Pharmacokinetic Model
• Solving Ordinary Differential Equations I
• Simulation and the Asymptotics of Optimization Estimators
• Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines
• Efficient Local Estimation for Time-Varying Coefficients in Deterministic Dynamic Models With Applications to HIV-1 Dynamics
• A Spline Least Squares Method for Numerical Parameter Estimation in Differential Equations
• Mathematical Analysis of HIV-1 Dynamics in Vivo
• Sieve Estimation for the Proportional-Odds Failure-Time Regression Model With Interval Censoring
• Estimation in a semiparametric model for longitudinal data with unspecified dependence structure
• Penalized regression with model-based penalties
• Parameter estimation of ordinary differential equations
• Ordinary Differential Equations in Theory and Practice
• Identifiability of nonlinear systems with application to HIV/AIDS models
• IDENTIFIABILITY OF HIV/AIDS MODELS
• Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models
• Statistical methods for HIV dynamic studies in AIDS clinical trials
• Hierarchical Bayesian Methods for Estimation of Parameters in a Longitudinal HIV Dynamic System
• Asymptotic Properties of Non-Linear Least Squares Estimators
• The Consistency of Nonlinear Regressions
• Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention
• Sieve Maximum Likelihood Estimator for Semiparametric Regression Models With Current Status Data
• Convergence of stochastic processes