• COMPARISON BETWEEN M-ESTIMATION, S-ESTIMATION, AND MM ESTIMATION METHODS OF ROBUST ESTIMATION WITH APPLICATION AND SIMULATION

EHAB MOHAMED ALMETWALLY*, HISHAM MOHAMED ALMONGY

Abstract


In regression analysis the use of ordinary least squares, (OLS) method would not be appropriate in solving problem containing outlier or extreme observations. Therefore, we need a method of robust estimation where the value of the estimation is not much affected with these outlier or extreme observations. In this paper, six methods of estimation will be compared in order to reach the best estimation, and these methods are M.Humpel estimation method, M.Bisquare estimation method, M.Huber estimation method, S-estimation method, MM(S)-estimation method, and MM estimation method in robust regression to determine a regression model. We find that, the best three method, through this study, are M-estimation method, MM(S)-estimation method and MM estimation method. Since M-estimation method is an extension of the maximum likelihood method, while MM estimation method is the development of M-estimation method and MM(S) estimation method is the development of S-estimation method. Robust regression methods can considerably improve estimation precision, but should not be applied automatically instead of the classical methods.


Keywords


Ordinary Least Squares, Robust Estimation, M-estimation, S-estimation, MM estimation and Monte Carlo simulation.

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