A non parametric estimation method using an orthogonal function system

Yue Feng, Yuanguo Zhu and Liu He

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 19, 6249-6263

Abstract: When modeling uncertain systems with uncertain differential equations (UDEs), it is a common thing that the relative function forms are unknown. In such cases, non parametric estimation based on observed data can be used to approximate the relative functions. This article presents a non parametric estimation method for nonautonomous UDEs utilizing an orthogonal function system, which proves to be beneficial in simulating uncertain non autonomous dynamical systems in practical applications. The reliability of the proposed method is validated through various examples. The approximation effects of different orthogonal basis functions are compared. Furthermore, the article illustrates the availability of the proposed method by using the closing price data of four stocks.

Date: 2025
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DOI: 10.1080/03610926.2025.2452209

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