Regression and correlation analyses of a linear relation between random intervals. (English) Zbl 0981.62062

Summary: We develop regression and correlation analyses of a certain general linear relation between two random elements whose values are non-empty compact intervals. To this purpose, we firstly extend the least-squares method to deal with the involved random elements on the basis of a generalized metric defined on the space of the considered intervals. As a complementary study, a coefficient quantifying the strength of the linear relation between the two random elements is also presented, and a discussion of the extreme values for this measure is presented. A real-life example illustrates these studies.


62J05 Linear regression; mixed models
62J99 Linear inference, regression
60D05 Geometric probability and stochastic geometry
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