Ordinary differential equation models for a collection of discretized functions
本文研究如何用常微分方程模型分析一组在离散时间点观测的函数，提出函数矩方法进行参数估计和曲线恢复，适用于稀疏到密集采样，涵盖非线性和非Lipschitz情形。
Abstract The exploration of dynamic systems governed by ordinary differential equations (ODEs) holds great interest in the field of statistics. Existing research mainly focuses on a single function. This study generalizes the scope to analyse a collection of functions observed at discretized times, with sampling frequencies varying from sparse to dense designs. The range of ODE models studied caters to diverse dynamic systems, and includes the complex nonlinear and non-Lipschitz scenarios. We introduce a new concept named functional moment method, a novel approach for parameter estimation within these ODE models and facilitating the recovery of curves for the discretely observed functions. Our numerical analysis underscores the method’s applicability across various application fields, including sociology, physics, and epidemiology.