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Estimation of a simple linear regression model for fuzzy random variables. (English) Zbl 1175.62073

Summary: A generalized simple linear regression statistical/probabilistic model where both input and output data can be fuzzy subsets of \(\mathbb R^p\) is dealt with. The regression model is based on a fuzzy-arithmetic approach and it considers the possibility of fuzzy-valued random errors. Specifically, the least-squares estimation problem in terms of a versatile metric is addressed. The solutions are established in terms of the moments of the involved random elements by employing the concept of support function of a fuzzy set. Some considerations concerning the applicability of the model are made.

MSC:

62J05 Linear regression; mixed models
62J86 Fuzziness, and linear inference and regression
62F10 Point estimation
62F86 Parametric inference and fuzziness
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