Semiparametric modeling of autonomous nonlinear dynamical systems with applications

In this paper, we propose a semi-parametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear semi-parametric mixed effects model. We also propose a computationally efficient model selection procedure. We prove consistency of the proposed estimator under suitable regularity conditions. We show by simulation studies that the proposed estimation as well as model selection procedures can efficiently handle sparse and noisy measurements. Finally, we apply the proposed method to a plant growth data used to study growth displacement rates within meristems of maize roots under two different experimental conditions.