Weighted Least Squares and Least Median Squares estimation for the fuzzy linear regression analysis

Pierpaolo D’Urso () and Riccardo Massari
Authors registered in the RePEc Author Service: Pierpaolo D'Urso

METRON, 2013, vol. 71, issue 3, 279-306

Abstract: In this paper, we discuss the problem of regression analysis in a fuzzy domain. By considering an iterative Weighted Least Squares estimation approach, we propose a general linear regression model for studying the dependence of a general class of fuzzy response variable, i.e., $$LR_2$$ L R 2 fuzzy variable or trapezoidal fuzzy variable,on a set of crisp or $$LR_2$$ L R 2 fuzzy explanatory variables. We also show some theoretical properties and a suitable generalization of the determination coefficient in order to investigate the goodness of fit of the regression model. Furthermore, we discuss some theoretical issues and an assessment of imprecision of the regression function. Finally, we suggest a robust version of the fuzzy regression model based on the Least Median Squares estimation approach which is able to neutralize and/or smooth the disruptive effects of possible crisp or fuzzy outliers in the estimation process. A simulation study and two empirical applications are presented. Copyright Sapienza Università di Roma 2013

Keywords: Fuzzy input/output data; Fuzzy linear regression analysis; Robust fuzzy linear regression; Weighted Least Squares (WLS); Least Median Squares (LMS) (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s40300-013-0025-9

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