We consider the problem of parameter estimation for a system of ordinary differential equations from
noisy observations on a solution of the system. In case the system is nonlinear, as it typically is
in practical applications, an analytic solution to it usually does not exist. Consequently,
straightforward estimation methods like the ordinary least squares method depend on repetitive use
of numerical integration in order to determine the solution of the system for a sequence of
parameter values and to find subsequently the parameter value that minimises the objective function.
This induces a huge computational load on such estimation methods. We propose an estimator that is
defined as a minimiser of an appropriate distance between a nonparametrically estimated derivative
of the solution and the right-hand side of the system applied to a nonparametrically estimated
solution. Our estimator bypasses numerical integration altogether and reduces the amount of
computational time drastically compared to ordinary least squares. Moreover, we show that under
suitable regularity conditions this estimation procedure leads to a -consistent estimator
of the parameter of interest.
Joint work with Chris Klaassen.