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Least absolute deviations estimation for uncertain regression with imprecise observations

Author

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  • Zhe Liu

    (Tsinghua University)

  • Ying Yang

    (Tsinghua University)

Abstract

Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares, mostly due to the elegant theoretical foundation and ease of implementation. However, in many cases, we can only get imprecise observation values and the assumptions upon which the least squares is based may not be valid. So this paper characterizes the imprecise data in terms of uncertain variables and proposes a novel robust approach under the principle of least absolute deviations to estimate the unknown parameters in uncertain regression models. Furthermore, some general estimate approaches are also explored. Finally, numerical examples illustrate that our estimate is more robust than the least squares implying it is more suitable to handle observations with outliers.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:1:d:10.1007_s10700-019-09312-w
    DOI: 10.1007/s10700-019-09312-w
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    References listed on IDEAS

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    1. Zahra Mohmmad Nejad & Alireza Ghaffari-Hadigheh, 2018. "A novel DEA model based on uncertainty theory," Annals of Operations Research, Springer, vol. 264(1), pages 367-389, May.
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    3. Waichon Lio & Baoding Liu, 2018. "Uncertain data envelopment analysis with imprecisely observed inputs and outputs," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 357-373, September.
    4. Huber, Peter J., 1987. "The place of the L1-norm in robust estimation," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 255-262, September.
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    Cited by:

    1. 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.
    2. Zhe Liu, 2021. "Uncertain growth model for the cumulative number of COVID-19 infections in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 229-242, June.
    3. Zhongfeng Qin & Qiqi Li, 2023. "An uncertain support vector machine with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 611-629, December.
    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. Liu, Zhe & Yang, Ying, 2022. "Moment estimation for parameters in high-order uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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