Time-course window estimator for ordinary differential equations linear in the parameters

In many applications obtaining ordinary differential equation descriptions of dynamic processes is scientifically important. In both, Bayesian and likelihood approaches for estimating parameters of ordinary differential equations, the speed and the convergence of the estimation procedure may crucially depend on the choice of initial values of the parameters. Extending previous work, we show in this paper how using window smoothing yields a fast estimator for systems that are linear in the parameters. Using weak assumptions on the measurement error, we prove that the proposed estimator is $$\sqrt{n}$$n-consistent. The estimator does not require an initial guess for the parameters and is computationally fast and, therefore, it can serve as a good initial estimate for more efficient estimators. In simulation studies and on real data we illustrate the performance of the proposed estimator.