A hybrid method based on \(F\)-transform for robust estimators. (English) Zbl 1458.62080
Summary: Robust regression analysis is a stable method to fit a given dataset especially when the data set includes outliers. It has been developed with various approaches due to its practical usefulness and insensitivity to outliers. In this paper, we propose a new hybrid algorithm based on several robust methods combined with \(F\) (fuzzy)-transform to compare its performances with several robust methods. Some \(M\)-estimators such as \(L_1\), \(L_1 - L_2\) and Fair have been used as existing robust methods. \(L_2\), which is very sensitive to outliers, also has been used for comparison. Additionally, the Orthogonal distance regression (ODR) is introduced to enhance the deficiency of basic distance of error. To find the estimated parameters which minimize the objective functions, the Genetic Algorithm (GA) is used as an optimization algorithm. The performances are measured in RMSE, MAD and MAPE to compare their accuracies. Three examples are provided and the results show that the proposed hybrid methods are much more superior to existing robust methods such as \(L_1\), \(L_1 - L_2\) and Fair.
MSC:
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 62F10 | Point estimation |
| 62F86 | Parametric inference and fuzziness |
Keywords:
robust estimators; \(M\)-estimators; \(F\)-transform; orthogonal distance regression (ODR); optimization algorithm; genetic algorithm (GA)References:
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