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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). ==Advantages== Redescending M-estimators have high breakdown points (close to 0.5), and their Ψ function can be chosen to redescend smoothly to 0. This means that moderately large outliers are not ignored completely, and greatly improves the efficiency of the redescending M-estimator. The redescending M-estimators are slightly more efficient than the Huber estimator for several symmetric, wider tailed distributions, but about 20% more efficient than the Huber estimator for the Cauchy distribution. This is because they completely reject gross outliers, while the Huber estimator effectively treats these the same as moderate outliers. As other M-estimators, but unlike other outlier rejection techniques, they do not suffer from masking effects. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Redescending M-estimator」の詳細全文を読む スポンサード リンク
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