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Modified maximum likelihood approach in uncertain regression analysis and application to factors analysis of urban air quality

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  • Liu, Yang
  • Qin, Zhongfeng

Abstract

Uncertain regression analysis is an indispensable field in statistics, and it conducts in-depth research on data sets under uncertain environments based on regression models to predict and explain the relationship between variables. However, when the data set is affected by outliers, the existing research methods will no longer be effective. In order to eliminate the influence of outliers on the accuracy of uncertain regression model fitting and prediction, this paper estimates the unknown parameters and disturbance term in the uncertain regression model based on a modified maximum likelihood idea, and provides a numerical algorithm to solve the specific estimator. Subsequently, two numerical examples are also provided to illustrate the modified maximum likelihood approach proposed in this paper and its effectiveness compared with the existing maximum likelihood method. Finally, this paper applies the proposed approach to the factor analysis of Shenzhen’s air quality, and successfully reveals the key factors affecting Shenzhen’s air quality, which provides a scientific basis for the subsequent management strategy.

Suggested Citation

  • Liu, Yang & Qin, Zhongfeng, 2025. "Modified maximum likelihood approach in uncertain regression analysis and application to factors analysis of urban air quality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 219-234.
    • Handle: RePEc:eee:matcom:v:234:y:2025:i:c:p:219-234
    DOI: 10.1016/j.matcom.2025.02.025
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    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. 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.
    7. 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.
    8. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    9. Dan Chen, 2023. "Uncertain regression model with moving average time series errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(21), pages 7632-7646, November.
    10. Tingqing Ye & Baoding Liu, 2023. "Uncertain significance test for regression coefficients with application to regional economic analysis," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(20), pages 7271-7288, October.
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