Examination of m-estimator for lineer regression model

Robust regression estimators have been developed to estimate regression model properly when errors have not normal distribution or there are outliers in data set.The objective of this thesis is an examination of M-estimators, one of robust regression estimators developed as an alternative to least squares estimator.Firstly, the sensitivity of iterative reweighted least squares algorithm to the choice of initial estimates is considered and the breakdown points of M-estimators are examined by means of plots. Next, when the distribution of error term is normal and different from normal, the performance of M-estimators is evaluated in terms of efficiency and finally contribution of initial scale estimator to efficiency is assessed. Also, M-estimators are applied on two real life examples and the obtained results are discussed.