A Method to Treat Some Dynamical Statistical Models

In this paper we present a method for the estimation of the parameters of models described by a nonlinear system of differential equations: we study the maximum likelihood estimator and the jackknife estimator for parameters of the system and for the covariance matrix of the state variables and we seek possible linear relations between parameters. We take into account the difficulty due to the small number of observations. The optimal experimental design for this kind of problem is determined. We give an application of this method for the glucose metabolism of goats.