Before revision:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these  estimators, we determine the finite sample breakdown point, the influence function, as well as  statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods. Finally, we check these asymptotic theoretical findings against finite sample behavior by an extensive simulation study  .
After revision:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the finite sample breakdown point, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking neighborhoods. These asymptotic findings are complemented by an extensive simulation study .