自治非线性动力系统的半参数建模及其应用
Semiparametric modeling of autonomous nonlinear dynamical systems with applications
摘要：
在本文中，我们提出了一个半参数模型的自治非线性动力系统，并设计了一个估计程序的模型拟合。该模型结合了受试者特异性效应，可视为非线性半参数混合效应模型。我们还提出了一个计算效率高的模型选择过程。在适当的正则条件下证明了估计量的相合性。我们通过仿真研究表明，所提出的估计以及模型选择程序可以有效地处理稀疏和噪声测量。最后，我们将所提出的方法应用于植物生长数据，用于研究在两种不同的实验条件下玉米根分生组织内的生长位移率。
英文摘要：
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.
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