Trimmed estimators in regression framework. (English) Zbl 1244.62099

Summary: From the practical point of view regression analysis and its least squares method is clearly one of the most used techniques of statistics. Unfortunately, if there is some problem present in the data (for example contamination), classical methods are not longer suitable. A lot of methods have been proposed to overcome these problematic situations. In this contribution we focus on a special kind of methods based on trimming. There exist several approaches which use trimming off part of the observations, namely the well known high breakdown point method least trimmed squares, least trimmed absolute deviation estimators or, e.g., the regression \(L\)-estimate trimmed least squares of R. Koenker and G. Bassett [seeEconometrica 46, 33–50 (1978; Zbl 0373.62038)]. Our goal is to compare these methods and its properties in detail.


62J05 Linear regression; mixed models
62G08 Nonparametric regression and quantile regression
62F10 Point estimation


Zbl 0373.62038
Full Text: EuDML


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