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 the complex non-linear 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 methods applicability across various application fields, including sociology, physics, and epidemiology.

Bio: 邵凌轩，本科期间就读于清华大学数学系学堂班，博士期间就读于北京大学数学与科学学院，后在复旦大学管理学院统计与数据科学系担任青年副研究员，同时兼任青年统计学家协会第二届理事会理事、中国现场统计研究会贝叶斯统计分会副秘书长。目前研究方向为变量重要性、复杂函数型数据分析等。邵凌轩已在期刊AoS，JRSSB，Bernoulli等期刊上发表多篇文章。