In case of unnormally distributed errors, alternative estimation methods in simple classic regression

Least Square Method is the most known and used method in the regression parametersestimate methods. Least Square Method require normaly distribute error to get thehypothesis tests and define the confidence intervals for estimators.When the distribution of the errors don?t satisfy the normal distribution, Least Squareestimators and hypothesis tests give wrong results.Beside this, when the data contain significant outliers Least Square estimators andhypothesis tests are influenced. In these situations, to reduce the effect of the outliers,more robust estimators which are influenced less from the deviations from theassumptions, can be used. Shortly, Robust Regression Methodology is the methodologywhich is offered to get more certain results, when Least Square Method don?t givereliable results.In this work, after the situations to use Robust Regression Methods are examined, LeastAbsolute Deviation Method which is named L1, and Huber?s M-Regression Method areexamined and Tukey?s, Hampel?s and Andrews?s M-type estimators approaches arediscussed. And an application is given for these methods.Keywords: Robust Regression, Least Absolute Deviation, Median Absolute Deviation,M- type estimators