**Redescending M-estimator**

In statistics, **Redescending M-estimators** are Ψ-type M-estimators which have ψ functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin. Their ψ functions can be chosen to redescend smoothly to zero, so that they usually satisfy ψ(x) = 0 for all x with |x| > r, where r is referred to as the minimum rejection point.

Due to these properties of the ψ 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. They are efficient because they completely reject gross outliers, and do not completely ignore moderately large outliers (like median).

Read more about Redescending M-estimator: Advantages, Disadvantages, Choosing Redescending Ψ Functions, Examples