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

Author

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  • 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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    References listed on IDEAS

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    1. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    2. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    3. Tingqing Ye & Baoding Liu, 2022. "Uncertain hypothesis test with application to uncertain regression analysis," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 157-174, June.
    4. Tingqing Ye & Xiangfeng Yang, 2021. "Analysis and prediction of confirmed COVID-19 cases in China with uncertain time series," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 209-228, June.
    5. Yang Liu & Baoding Liu, 2024. "A modified uncertain maximum likelihood estimation with applications in uncertain statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(18), pages 6649-6670, September.
    6. Yang Liu & Baoding Liu, 2024. "Estimation of uncertainty distribution function by the principle of least squares," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(21), pages 7624-7641, November.
    7. Liu, Z. & Yang, Y., 2021. "Selection of uncertain differential equations using cross validation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    8. Zhe Liu & Ying Yang, 2020. "Least absolute deviations estimation for uncertain regression with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 33-52, March.
    9. Jianhua Ding & Hongyu Zhang & Zhiqiang Zhang, 2023. "Inferences for uncertain nonparametric regression by least absolute deviations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(16), pages 5640-5649, August.
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