High Quality Content by WIKIPEDIA articles! Redescending M-estimators are very popular ?-type M-estimators which have ? functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin. Their ? functions can be chosen to redescend smoothly to zero, so that they usually satisfy ?(x) = 0 for all x with |x| > r, where r is referred to as the minimum rejected point. Due to these properties of the ? function, these kinds of estimators are very efficient, have a high breakdown point, and, unlike other outlier rejection techniques, they do not suffer from a masking effect. Their efficiency results from the fact that they completely reject gross outliers, and do not completely ignore moderately large outliers (like median).

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