We propose a semiparametric 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 semiparametric mixed effects model. We also propose a computationally efficient model selection procedure. 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.
"Semiparametric modeling of autonomous nonlinear dynamical systems with application to plant growth." Ann. Appl. Stat. 5 (3) 2078 - 2108, September 2011. https://doi.org/10.1214/11-AOAS459