Robust Estimation Using M Estimation and S Estimation

Main Article Content

นิธิภัทร กมลสุข


In linear regression analysis, the ordinary least squares (OLS) estimators of parameters have always turned out to be the best linear unbiased estimators. However, if the data contain outliers, this may affect the least-squares estimates. So, an alternative approach; the so-called robust regression methods, is needed to obtain a better fit of the model or more precise estimates of parameters. In this article, various robust regression methods have been reviewed. The focus is on the robust estimation using M estimation and S estimation.


Article Details

How to Cite
กมลสุขน. (2018). Robust Estimation Using M Estimation and S Estimation. KASALONGKHAM RESEARCH JOURNAL, 12(2), 55-68. Retrieved from


Koller, M., & Stahel, W. A. (2011). Sharpening wald-type inference in robust regression for small samples. Computational Statistics & Data Analysis, 55(8), 2504-2515.

Massart, D. L., & Kaufman, L., M., Rousseeuw, P. J., & Leroy, A. (1986). Least median of squares: A robust method for outlier and model error detection in regression and calibration. Analytica Chimica Acta, 187, 171-179.

Milhano, T., Sequera, J., & Sotto, E. D. (2013). Using S-estimators in Parameter Identification . In Proceedings of the Information Fusion International Conference 2013, (pp. 1058-1065). Istanbul: Turkey.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2006). Introductions to Linear
Regression Analysis (4th ed.). New York: John Wiley & Sons.

Nguyen, T. D., and Welsch, R. (2010). Outlier detection and least trimmed
squares approximation using semidefinite programming. Computational
Statistics & Data Analysis, 54, 3212–3226.

Ollerer, V., Alfons, A., & Croux, C. (2016). The shooting S-estimator for robust regression. Computational Statistical, 31(3), 829-844.

Panik, M. (2009). Regression Modeling Methods, Theory, and Computation with
SAS. New York: Taylor & Francis Group.

Rousseeuw, P., & Yohai, V. (1984). Robust regression by means of S-estimators Robust and nonlinear time series analysis (pp. 256-272): Springer.

Rousseeuw, P. J., & Leroy, A. M. (2003). Robust regression and outlier detection (Vol. 589): John wiley & sons.

Smirnov, P. O., & Shevlyakov, G. L. (2014). Fast highly efficient and robust one-step M-estimators of scale based on Qn. Computational Statistics & Data Analysis, 78, 153-158.

Susanti, Y., & Pratiwi, H. (2014). M estimation, S estimation, and MM estimation in robust regression. International Journal of Pure and Applied Mathematics, 91(3), 349-360.

Thomas, L., & Mili, L. (2007). A Robust GM-Estimator for the Automated
Detection of External Defects on Barked Hardwood Logs and Stems.

Yarmohammadi, M., & Mahmoudvand, R. (2010). The Effect Of Outliers On Robust And Resistant Coefficient Of Determination In The Linear Regression Models. International Journal of Academic Research, 2(3).