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Uncertain hypothesis test with application to uncertain regression analysis

Author

Listed:
  • Tingqing Ye

    (Tsinghua University)

  • Baoding Liu

    (Tsinghua University)

Abstract

This paper first establishes uncertain hypothesis test as a mathematical tool that uses uncertainty theory to help people rationally judge whether some hypotheses are correct or not, according to observed data. As an application, uncertain hypothesis test is employed in uncertain regression analysis to test whether the estimated disturbance term and the fitted regression model are appropriate. In order to illustrate the test process, some numerical examples are documented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:2:d:10.1007_s10700-021-09365-w
    DOI: 10.1007/s10700-021-09365-w
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    References listed on IDEAS

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    1. Jianhua Ding & Zhiqiang Zhang, 2021. "Statistical inference on uncertain nonparametric regression model," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 451-469, December.
    2. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. 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.
    4. Waichon Lio & Baoding Liu, 2021. "Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 177-188, June.
    5. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    6. Xiangfeng Yang & Baoding Liu, 2019. "Uncertain time series analysis with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 263-278, September.
    7. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. Xiangfeng Yang & Hua Ke, 2023. "Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 447-462, September.
    2. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    3. 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.
    4. Liu He & Yuanguo Zhu & Yajing Gu, 2023. "Nonparametric estimation for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 697-715, December.
    5. Tingting Yang & Xiaoxia Huang, 2022. "A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 723-747, November.
    6. Li, Bo & Lu, Ziqiang, 2023. "Uncertain random enhanced index tracking for portfolio selection with parameter estimation and hypothesis test," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    7. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    8. Chen, Wen-Bin & Li, Xiao-Yang & Wu, Ji-Peng & Kang, Rui, 2024. "Uncertain random accelerated degradation modelling and statistical analysis with aleatory and epistemic uncertainties from multiple dimensions," Reliability Engineering and System Safety, Elsevier, vol. 243(C).

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