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Estimation problems in two types of uncertain varying coefficient models with imprecise observations

Author

Listed:
  • Yuxuan Zhang

    (Xinjiang University)

  • Zhiming Li

    (Xinjiang University)

Abstract

The varying coefficient model mitigates the curse of dimensionality in nonparametric regression as the number of explanatory variables increases. To address high-dimensional uncertain phenomena characterized by imprecise observations, this paper introduces two uncertain varying coefficient models, employing uncertain variables for robust modeling. Based on the least squares method, we use local linear and B-spline estimations for the two models with crisp and uncertain explanatory variables. To account for potential differences in smoothness among various coefficient functions, we propose two-step estimation procedures based on the two approaches to improve the fitting accuracy. In addition, residual analysis and uncertain hypothesis testing are performed to evaluate the suitability of the fitted model. Two numerical examples and an application involving weather data demonstrate the effectiveness of these methods.

Suggested Citation

  • Yuxuan Zhang & Zhiming Li, 2025. "Estimation problems in two types of uncertain varying coefficient models with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 24(2), pages 223-249, June.
    • Handle: RePEc:spr:fuzodm:v:24:y:2025:i:2:d:10.1007_s10700-025-09444-2
    DOI: 10.1007/s10700-025-09444-2
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