caa a22 4500 605461937 CHVBK 20210128100245.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10114-015-4256-y doi (NATIONALLICENCE)springer-10.1007/s10114-015-4256-y Numerical discretization-based kernel type estimation methods for ordinary differential equation models [Elektronische Daten] [Tao Hu, Yan Qiu, Heng Cui, Li Chen] We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation (ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method (kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method (Eulers discretization method, the trapezoidal discretization method, or the Runge-Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost. Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Nonparametric regression nationallicence kernel smoothing nationallicence local polynomial fitting nationallicence parametric identification nationallicence ordinary differential equation nationallicence numerical discretization nationallicence two-stage method nationallicence Hu Tao School of Mathematical Sciences & BCMIIS, Capital Normal University, 100048, Beijing, P. R. China aut Qiu Yan School of Mathematical Sciences, Beijing Normal University, 100875, Beijing, P. R. China aut Cui Heng School of Mathematical Sciences & BCMIIS, Capital Normal University, 100048, Beijing, P. R. China aut Chen Li Fujian College of Water Conservancy and Eletric Power, 366000, Fujian, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1233-1254 1439-8516 31:8<1233 2015 31 10114 https://doi.org/10.1007/s10114-015-4256-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4256-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hu Tao School of Mathematical Sciences & BCMIIS, Capital Normal University, 100048, Beijing, P. R. China aut NATIONALLICENCE 700 1- Qiu Yan School of Mathematical Sciences, Beijing Normal University, 100875, Beijing, P. R. China aut NATIONALLICENCE 700 1- Cui Heng School of Mathematical Sciences & BCMIIS, Capital Normal University, 100048, Beijing, P. R. China aut NATIONALLICENCE 700 1- Chen Li Fujian College of Water Conservancy and Eletric Power, 366000, Fujian, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1233-1254 1439-8516 31:8<1233 2015 31 10114