Comparison of M, MM and LTS estimators in linear regression in the presence of outlier

Authors: CEM TIRINK, HASAN ÖNDER

Abstract: In this study, it was aimed to evaluate the performance of different estimators that will be used in regression analysis, which is one of the multivariate statistical methods in the presence of outliers in the data set. Sixth month live weight was estimated with various body measurements for Saanen kids taken from a private farm. In the data set, the use and performance of robust estimators were evaluated because the least squares method did not provide reliable results in the case of outliers. M (for Huber and Tukey bisquare) estimator, MM estimator and LTS estimator were used as robust used in the presence of outliers. MSE, RMSE, rRMSE, MAPE, MAD, R$^{2}$ , R$^{2}$ $_{adj}$ and AIC were used as model comparison criteria in the study. As a result of the study, in the case of outlier in the data set, Huber type M estimator can be recommended.

Keywords: Least squares, outliers, robust estimator, Saanen

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