Quantile-Based Fuzzy Semi-Parametric Support Vector Regression Model Based on Autoregressive Fuzzy Terms: An Estimation Approach

The semi-parametric regression model is one of the most useful statistical tools that has gained significant attention recently due to its key capability of combining both parametric and nonparametric features in one model. In practical applications, however, the recorded information or the relationship between one or more independent variables and the dependent variable is typically imprecise. Additionally, in certain situations, the error terms exhibit heteroscedasticity or the data distribution is skewed, which leads to inaccurate results when using conventional least squares models. In this regard, this paper introduces a semi-parametric quantile-based regression model using the support vector machine technique, along with precise regressors and fuzzy outcomes. We also employ the classic Durbin-Watson test to explore the existence of correlation among fuzzy residual expressions. We propose a mixed procedure that incorporates a mean absolute error and a cross-validation measure to calculate fuzzy multipliers in addition to the unknown autocorrelation criteria. We illustrate the efficacy of the suggested method via three numerical examples, including two applied examples and a simulation study. To this end, we use some common goodness-of-fit measurements to assess the performance of the suggested method in comparison with other approaches. The numerical results showed that when the fuzzy error terms are correlated, the suggested fuzzy semi-parametric quantile-based regression model performs better than the other methods.