M Estimation, s estimation, and mm estimation in robust regression

Abstract

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.