Hypotheses testing for fuzzy robust regression parameters

The classical least squares (LS) method is widely used in regression analysis because computing its estimate is easy and traditional. However, LS estimators are very sensitive to outliers and to other deviations from basic assumptions of normal theory [Huynh H. A comparison of four approaches to robust regression. Psychol Bull 1982;92:505–12; Stephenson D. 2000. Available from: http://folk.uib.no/ngbnk/kurs/notes/node38.html; Xu R, Li C. Multidimensional least-squares fitting with a fuzzy model. Fuzzy Sets and Systems 2001;119:215–23.]. If there exists outliers in the data set, robust methods are preferred to estimate parameters values. We proposed a fuzzy robust regression method by using fuzzy numbers when x is crisp and Y is a triangular fuzzy number and in case of outliers in the data set, a weight matrix was defined by the membership function of the residuals. In the fuzzy robust regression, fuzzy sets and fuzzy regression analysis was used in ranking of residuals and in estimation of regression parameters, respectively [Şanlı K, Apaydin A. Fuzzy robust regression analysis based on the ranking of fuzzy sets. Inernat. J. Uncertainty Fuzziness and Knowledge-Based Syst 2008;16:663–81.]. In this study, standard deviation estimations are obtained for the parameters by the defined weight matrix. Moreover, we propose another point of view in hypotheses testing for parameters.