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Robust regression for interval-valued data based on midpoints and log-ranges

Author

Listed:
  • Qing Zhao

    (Beihang University
    Beihang University)

  • Huiwen Wang

    (Beihang University
    Beihang University)

  • Shanshan Wang

    (Beihang University
    Beihang University)

Abstract

Flexible modelling of interval-valued data is of great practical importance with the development of advanced technologies in current data collection processes. This paper proposes a new robust regression model for interval-valued data based on midpoints and log-ranges of the dependent intervals, and obtains the parameter estimators using Huber loss function to deal with possible outliers in a data set. Besides, the use of logarithm transformation avoids the non-negativity constraints for the traditional modelling of ranges, which is beneficial to the flexible use of various regression methods. We conduct extensive Monte Carlo simulation experiments to compare the finite-sample performance of our model with that of the existing regression methods for interval-valued data. Results indicate that the proposed method shows competitive performance, especially in the data set with the existence of outliers and the scenarios where both midpoints and ranges of independent variables are related to those of the dependent one. Moreover, two empirical interval-valued data sets are applied to illustrate the effectiveness of our method.

Suggested Citation

  • Qing Zhao & Huiwen Wang & Shanshan Wang, 2023. "Robust regression for interval-valued data based on midpoints and log-ranges," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 583-621, September.
    • Handle: RePEc:spr:advdac:v:17:y:2023:i:3:d:10.1007_s11634-022-00518-2
    DOI: 10.1007/s11634-022-00518-2
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    References listed on IDEAS

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    1. Paolo Giordani, 2015. "Lasso-constrained regression analysis for interval-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(1), pages 5-19, March.
    2. Paula Brito & A. Pedro Duarte Silva, 2012. "Modelling interval data with Normal and Skew-Normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 3-20, March.
    3. Hao, Peng & Guo, Junpeng, 2017. "Constrained center and range joint model for interval-valued symbolic data regression," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 106-138.
    4. Dias, Sónia & Brito, Paula, 2017. "Off the beaten track: A new linear model for interval data," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1118-1130.
    5. Maria Ferraro & Paolo Giordani, 2012. "A multiple linear regression model for imprecise information," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1049-1068, November.
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