PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Parameter estimation of ODE’s via nonparametric estimators
Nicolas J-B. Brunel
Electronic Journal of Statistics Volume 2, pp. 1242-1267, 2008.

Abstract

Ordinary differential equations (ODE’s) are widespreadmodels in physics, chemistry and biology. In particular, this mathematical formal- ism is used for describing the evolution of complex systems and it might consist of high-dimensional sets of coupled nonlinear differential equations. In this setting, we propose a general method for estimating the parame- ters indexing ODE’s from times series. Our method is able to alleviate the computational difficulties encountered by the classical parametricmethods. These difficulties are due to the implicit definition of the model.We propose the use of a nonparametric estimator of regression functions as a first-step in the construction of an M-estimator, and we show the consistency of the derived estimator under general conditions. In the case of spline estimators, we prove asymptotic normality, and that the rate of convergence is the usual root n-rate for parametric estimators. Some perspectives of refinements of this new family of parametric estimators are given.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:5221
Deposited By:Nicolas Brunel
Deposited On:24 March 2009