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Multiple linear regression models for random intervals: a set arithmetic approach

Author

Listed:
  • Marta García-Bárzana

    (ArcelorMittal)

  • Ana Belén Ramos-Guajardo

    (Oviedo University)

  • Ana Colubi

    (Justus Leibig Univerity Giessen)

  • Erricos J. Kontoghiorghes

    (Queen Mary University of London)

Abstract

Some regression models for analyzing relationships between random intervals (i.e., random variables taking intervals as outcomes) are presented. The proposed approaches are extensions of previous existing models and they account for cross relationships between midpoints and spreads (or radii) of the intervals in a unique equation based on the interval arithmetic. The estimation problem, which can be written as a constrained minimization problem, is theoretically analyzed and empirically tested. In addition, numerically stable general expressions of the estimators are provided. The main differences between the new and the existing methods are highlighted in a real-life application, where it is shown that the new model provides the most accurate results by preserving the coherency with the interval nature of the data.

Suggested Citation

  • Marta García-Bárzana & Ana Belén Ramos-Guajardo & Ana Colubi & Erricos J. Kontoghiorghes, 2020. "Multiple linear regression models for random intervals: a set arithmetic approach," Computational Statistics, Springer, vol. 35(2), pages 755-773, June.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00910-1
    DOI: 10.1007/s00180-019-00910-1
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    References listed on IDEAS

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    3. Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2016. "An exploratory data analysis in scale-space for interval-valued data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2643-2660, October.
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    Cited by:

    1. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.

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