In this research, some robust non-parametric methods were used to estimate the semi-parametric regression model, and then these methods were compared using the MSE comparison criterion, different sample sizes, levels of variance, pollution rates, and three different models were used. These methods are S-LLS S-Estimation -local smoothing, (M-LLS)M- Estimation -local smoothing, (S-NW) S-Estimation-NadaryaWatson Smoothing, and (M-NW) M-Estimation-Nadarya-Watson Smoothing.
The results in the first model proved that the (S-LLS) method was the best in the case of large sample sizes, and small sample sizes showed that the (M-LLS) method was the best, while the second model showed in general that the S-LLS method was the best in addition to the method M-LLS was the best in some cases of sample sizes and at different levels of variance. As for the third model, it was shown through the results that in most cases the S-LLS method was the best in addition to the M-LLS method which was better in some cases of sample sizes and at different levels of variance.
