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trimmed mean; least trimmed squares; least trimmed absolute deviations; trimmed LSE; regression quantiles
From the practical point of view the 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 special kind of methods based on trimming. There exist several approaches which use trimming off part of the observations, namely well known high breakdown point method the Least Trimmed Squares, Least Trimmed Absolute Deviation estimator or e.g. regression $L$-estimate Trimmed Least Squares of Koenker and Bassett. Our goal is to compare these methods and its properties in detail.
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