Optimal rate of direct estimators in systems of ordinary differential equations linear in functions of the parameters

Many phenomena in biology, chemistry, physics, and engineering are modeled by a system of possibly nonlinear ordinary differential equations that are linear in their unknown constants. Current methods to estimate these parameters are computationally extremely intensive. In this paper estimators are presented that reduce the computational burden dramatically and that have desirable statistical properties. Their $\sqrt n$-consistency is proved and simulation results illustrate their finite sample performance.