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Title: Multiple linear regression models for random intervals: a set arithmetic approach
Authors: Colubi, Ana 
Garciá-Bárzana, Marta 
Kontoghiorghes, Erricos John 
Ramos-Guajardo, Ana Belén 
Major Field of Science: Social Sciences
Field Category: Economics and Business
Keywords: Interval-valued data;Least-squares estimators;Linear modelling;Multiple regression;Set arithmetic
Issue Date: 1-Jun-2020
Source: Computational Statistics, 2020, vol. 35, no. 2, pp. 755-773
Volume: 35
Issue: 2
Start page: 755
End page: 773
Journal: Computational Statistics 
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.
ISSN: 0943-4062
DOI: 10.1007/s00180-019-00910-1
Rights: © Springer
Type: Article
Affiliation : Korea University 
Cyprus University of Technology 
University of Oviedo 
Justus Leibig Univerity Giessen 
Queen Mary University of London 
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