In regression analysis, the use of the ordinary least squares (OLS) method is inadvisable when dealing with outlier or extreme observations. As a result, we require a method of robust estimation in which the estimation value is not significantly affected by outlier or extreme observations. Four methods of estimation will be compared in this paper in order to determine the best estimation: the M estimation method, the Least Trimmed Square Estimator, the S-estimation method, and the MM estimation method in robust regression. We discover that the best method is the MM-estimation method in this study. The M-estimation method is an extension of the maximum likelihood method, whereas the MM estimation method is a development of the M-estimation method, and the S-estimation method is related to the M-estimation method due to the use of the M-estimation residual scale. While robust regression methods can significantly improve estimation precision, they should not be used in place of more traditional methods.
Date of Degree
Master of Science (MS)
Program of Study
Mathematics and Statistics
Science, Engineering and Technology
Morrison, T. S. (2021). Comparing various robust estimation techniques in regression analysis [Master’s thesis, Minnesota State University, Mankato]. Cornerstone: A Collection of Scholarly and Creative Works for Minnesota State University, Mankato. https://cornerstone.lib.mnsu.edu/etds/1179
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