Parameter Estimation by Fuzzy Adaptive Networks and Comparison with Robust Regression Methods

Abstract

Fuzzy adaptive networks used for estimating the unknown parameters of a regression model are based on fuzzy ifthen rules and a fuzzy inference system. In regression analysis, data analysis is very important, because, every observation may have a large influence on the parameters estimates in the regression model. When a data set has outliers, robust methods such as the M method (Huber, Hampel, Andrews and Tukey), Least Median of Squares (LMS) and Reweighed Least Squares Based on the LMS (RLS) are used for estimating parameters. In this study, a method and an algorithm have been suggested to define the parameters of a switching regression model. Adaptive networks have been used in constructing one model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, to define the optimal class number of independent variables, we aimed to use the suggested validity criterion. The proposed method has the properties of a robust method, because the process does not give permission to the intuitional and is not affected by the outliers, which exist in the independent variable. Consequently, another aim of this study is, to compare the proposed method with the robust methods that are mentioned above. For the comparison the cross-validation method is used.