Estimation of Differential Equations via Nonparametric Methods: Applications in Systems Biology
Differential equations are widely used in experimental sciences. Nevertheless, the estimation of the parameters indexing the equations still generates important computational difficulties (huge computational times, local maxima) when using classical methods (least squares, likelihood). We study the use of nonparametric estimators of the solution and of its derivative for the construction of M-estimators easier to compute. We show that the parametric estimator is consistent and asymptotically normal under simple conditions, but the rate of convergence remains nonparametric. We propose then some procedures for ameliorating the asymptotic behavior and for integrating prior knowledge.