Affiliations: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, China
Correspondence:
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Corresponding author. Yuanguo Zhu, School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, China. E-mail: ygzhu@njust.edu.cn.
Abstract: In recent years, there has been a great development in parameter estimation methods for uncertain differential equations (UDEs). However, the observations we can obtain in real life are limited, in which case the form of function in a UDE is unknown. When dealing with such UDEs, we may use observational data to make nonparametric estimates. There are many nonautonomous systems in real life, and nonautonomous UDEs can simulate some uncertain nonautonomous dynamical systems well. In this paper, a nonparametric estimation method based on the nonautonomous UDEs of the binary Legendre polynomial is proposed. Then, three numerical examples are given to verify the reliability of nonparametric estimation. As an application, a real data example of global average monthly temperatures is used to illustrate the effectiveness of our method.
Keywords: Uncertainty theory, uncertain differential equations, nonparametric estimation, global average monthly temperature
