A0375
Title: Ordinary differential equation models for a collection of discretized functions
Authors: Lingxuan Shao - Fudan University (China) [presenting]
Fang Yao - Peking University, University of Toronto (Canada)
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 analyze 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 complex, non-linear, and non-Lipschitz scenarios. A new concept is introduced, named the functional moment method, a novel approach for parameter estimation within these ODE models and facilitating the recovery of curves for the discretely observed functions. The numerical analysis underscores the method's applicability across various application fields, including sociology, physics, and epidemiology.
