M Estimation, S Estimation, and Mm Estimation in Robust Regression

In regression analysis the use of least squares method would not be appropriate in solving problem containing outlier or extreme observations. So we need a parameter estimation method which is robust where the value of the estimation is not much affected by small changes in the data. In this paper we present M estimation, S estimation and MM estimation in robust regression to determine a regression model. M estimation is an extension of the maximum likelihood method and is a robust estimation, while S estimation and MM estimation are the development of M estimation method. The algorithm of these methods is presented and then we apply them on the maize production data.