Abstract
The linear regression problem of a fuzzy response variable on a set of real and/or fuzzy explanatory variables is investigated. The notion of LR fuzzy random variable is introduced in this connection, leading to the probabilization of the center and the left and right spreads of the response variable. A specific metric is suggested for coping with this type of variables. A class of linear regression models is then proposed for the center and for suitable transforms of the spreads in order to satisfy the nonnegativity conditions for the latter ones. A Least Squares solution for estimating the parameters of the models is derived, along with a goodness-of-fit measure and the associated hypothesis testing procedure. Finally, the results of a real-life application are illustrated.
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Coppi, R., Ferraro, M.B., Giordani, P. (2013). A Class of Linear Regression Models for Imprecise Random Elements. In: Torelli, N., Pesarin, F., Bar-Hen, A. (eds) Advances in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35588-2_20
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DOI: https://doi.org/10.1007/978-3-642-35588-2_20
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