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

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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.

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Acknowledgements

The research in this paper has been partially supported by the Spanish Government through MINECO-18-MTM2017-89632-P Grant and by the COST Action 1408. Their financial support is greatfully acknowledged.

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Authors and Affiliations

  1. Reasearch and Development Department, ArcelorMittal, Asturias, Spain

    Marta García-Bárzana

  2. Department of Statistics, Oviedo University, Oviedo, Spain

    Ana Belén Ramos-Guajardo

  3. Justus Leibig Univerity Giessen, Giessen, Germany

    Ana Colubi

  4. School of Economics and Finance, Queen Mary University of London, London, UK

    Erricos J. Kontoghiorghes

Authors
  1. Marta García-Bárzana
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  2. Ana Belén Ramos-Guajardo
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  3. Ana Colubi
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  4. Erricos J. Kontoghiorghes
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Correspondence to Ana Belén Ramos-Guajardo.

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García-Bárzana, M., Ramos-Guajardo, A.B., Colubi, A. et al. Multiple linear regression models for random intervals: a set arithmetic approach. Comput Stat 35, 755–773 (2020). https://doi.org/10.1007/s00180-019-00910-1

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