Ordinary differential equation models for a collection of discretized functions

• 成果类型: Article
• 署名作者: Shao, Lingxuan; Yao, Fang
• 署名单位: Fudan University; Peking University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkaf036
• 发表日期: 2025-11
• 页码: 1707-1724
• 关键词: curve recovery; functional moment method; Functional principal component analysis; parameter detection; regression; SPARSE

摘要

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.