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We investigate two important properties of M-estimators, namely, robustness and tractability, in the linear regression setting, when the observations are contaminated by some arbitrary outliers. Specifically, robustness means the statistical property that the estimator should always be close to the true underlying parameters regardless of the distribution of the outliers, and tractability indicates the computational property that the estimator can be computed efficiently, even if the objectivedoi:10.5705/ss.202019.0324 fatcat:nc2gslz5srhkpcuavilyvzvvxq