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Abstract An improved resampling algorithm for S estimators reduces the number of times the objective function is evaluated and increases the speed of convergence. With this algorithm, S estimates can be computed in less time than least median squares (LMS) for regression and minimum volume ellipsoid (MVE) for location/scatter estimates with the same accuracy. Here accuracy refers to the randomness due to the algorithm. S estimators are also more statistically efficient than the LMS and MVE estimators, that is, they have less variability due to the randomness of the data.
David Ruppert (Tue,) studied this question.