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A non parametric estimation method using an orthogonal function system

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  • Yue Feng
  • Yuanguo Zhu
  • Liu He

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.

Suggested Citation

  • Yue Feng & Yuanguo Zhu & Liu He, 2025. "A non parametric estimation method using an orthogonal function system," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(19), pages 6249-6263, October.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:19:p:6249-6263
    DOI: 10.1080/03610926.2025.2452209
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