M-estimators using optimization algorithm based on F-transform

Robust estimation is an estimation technique which is insensitive to small departures from the idealized assumptions, especially inclusion of outliers of the data set. One of the popular robust technique is the so-called M-estimators. In a practical sense, there are many cases when the data set includes outliers, robust technique has been developed with various approaches due to its practical usefulness. In this paper, we propose a new algorithm based on F(Fuzzy)-transform and optimization algorithm, a modified GA (Genetic Algorithm). For this, two approaches are considered for comparison in order to minimize the objective functions of several robust M-estimators such as L
₁
, L
₁
- L
₂
and Fair methods. One is a method which employs GA(Genetic Algorithm) as an optimization algorithm for minimization of the objective functions and the other one is a combined method based on F-transform and GA(Genetic Algorithm)which improves the accuracies. For a numerical example, the results are given with L
₂
(Least-squares) method, which is most popular but sensitive to outliers, for comparison. The performances are measured in RMSE, MAD and MAPE to show its superiority.