A robust varying coefficient approach to fuzzy multiple regression model

The varying coefficient models are powerful tools for exploring the dynamic pattern between a response and a group of predictors in multiple regression models. In addition, robust regression is another solid approach in the regression analyses for cases whose data are contaminated with outliers or influential observations. This paper proposed a novel varying coefficient model with exact predictors and fuzzy responses which can be used in cases where outliers occur in the data set. For this purpose, a locally weighted approximation idea and a popular M-estimator were combined to estimate unknown fuzzy (nonparametric) varying coefficients. Some common goodness-of-fit criteria including an outlier detection criterion were also applied to examine the performance of the proposed method. The effectiveness of the presented method was then illustrated through two numerical examples including a simulation study. It was also compared with several common fuzzy multiple regression models. The numerical results clearly indicate that the proposed method is not sensitive to the outliers. Moreover, compared to the available fuzzy multiple regressions with constant coefficients, the proposed fuzzy varying coefficient model managed to provide more accurate results. (C) 2019 Elsevier B.V. All rights reserved.