Green's matching: an efficient approach to parameter estimation in complex dynamic systems

• 成果类型: Article
• 署名作者: Tan, Jianbin; Zhang, Guoyu; Wang, Xueqin; Huang, Hui; Yao, Fang
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Sun Yat Sen University; Peking University; Renmin University of China
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae031
• 发表日期: 2024
• 页码: 1266-1285
• 关键词: ordinary differential-equations; regression; MODEL

摘要

Parameters of differential equations are essential to characterize intrinsic behaviours of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green's matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate trajectories in dynamic systems but not their derivatives due to the inverse of differential operators by Green's function. This yields a statistically optimal guarantee for parameter estimation in general-order equations, a feature not shared by existing methods, and provides an efficient framework for broad statistical inferences in complex dynamic systems.