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A set arithmetic-based linear regression model for modelling interval-valued responses through real-valued variables. (English) Zbl 1321.62078

Summary: A new linear regression model for an interval-valued response and a real-valued explanatory variable is presented. The approach is based on the interval arithmetic. Comparisons with previous methods are discussed. The new linear model is theoretically analyzed and the regression parameters are estimated. Some properties of the regression estimators are investigated. Finally, the performance of the procedure is illustrated using both a real-life application and simulation studies.

MSC:

62J05 Linear regression; mixed models
62F10 Point estimation
65C60 Computational problems in statistics (MSC2010)
65G30 Interval and finite arithmetic
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