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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\u2019s 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\u2019s 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.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae031","type":"journal-article","created":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T12:10:41Z","timestamp":1712923841000},"page":"1266-1285","source":"Crossref","is-referenced-by-count":5,"title":["Green\u2019s matching: an efficient approach to parameter estimation in complex dynamic systems"],"prefix":"10.1093","volume":"86","author":[{"given":"Jianbin","family":"Tan","sequence":"first","affiliation":[{"name":"International Institute of Finance, School of Management, University of Science and Technology of China , Hefei, Anhui ,","place":["People\u2019s Republic of China"]},{"name":"School of Mathematics, Sun Yat-sen University , Guangzhou, Guangdong ,","place":["People\u2019s Republic of 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