Comparison of Adaptive and M Estimation in Linear Regression

In the presence of outliers least square estimation is insufficient and can be biased. Adaptive estimation is robust estimation that can be used to improve the accuracy of the estimate by reducing the influence of outliers. Adaptive estimators can be effective in achieving low mean squared error for a variety of non normal distributions of errors. M estimation is the extension of the maximum likelihood estimation and is also a robust estimation. In this paper, comparison is made between OLS Estimation, Adaptive estimation and M estimation under a particular situation (An example).