The comparison of the iteration methods used in parameter estimation

In this thesis the comparison of the iteration methods for the estimation of the parameters of the general linear regression models via simulation is aimed. The relative efficiencies of the used methods with respect to the least squares (LS) method are calculated and interpreted while being formatted as tables. The Huber M, the Tukey M, the S and the MM were included in the study. The programs of all of the methods were written by using Matlab. As expected, in general, the MM estimators are found to be the most efficient estimators depending on the simulation results. Again as expected, the S estimators are found to be less efficient than the other iterative methods. The LS estimators are while naturally being more efficient under normality than the other methods, they are less efficient under the other models. In this study, one of the most important results appeared in the estimation of the variance of the error term. While the LS estimator of the variance of the error term is unbiased, the other estimators produce bias. The MM estimator of the variance is, as a different feature from the others while being biased, less biased and asymptotically it responses better in reducing the bias. At the end of the study, two real life data examples were given with the estimated values of each method. For both examples, various criteria and graphs were utilized.