The Breakdown Points of the Mean Combined with Some Rejection Rules

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Abstract
In the past, methods for rejection of outliers have been investigated mostly without regard to the quantitative consequences for subsequent estimation or testing procedures. Moreover, although rejection of outliers with subsequent application of least squares methods is one of the oldest and most widespread classes of robust procedures, until recently no comparison was made with other robust methods. In this article the simplest situation, namely estimation of a location parameter in the potential presence of outliers, is treated by means of a Monte Carlo study. This study yields Monte Carlo variances of the “arithmetic mean” after rejection of outliers according to several classical and recent formal rules. The results are also compared with those for other robust estimators of location parameters. It turns out that a simple summary and theoretical explanation of the Monte Carlo results is provided by the breakdown points of the combined rejection-estimation procedures. As a by-product, the concept of br...

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