Using angles to identify concentrated multivariate outliers

This article describes a procedure for the detection of multivariate outlie rs based on the analysis of certain angular properties of the observations. The method is simple. exploratory in nature, and particularly well suited for the detection of concentrated contamination patterns, in which the outl iers appear to form a cluster, separated from the sample. It is shown that it presents good properties for the identification of contaminations on hig h-dimensional sample spaces and for high contamination levels, including so me cases in which methods based on robust estimators (the minimum covarianc e determinant and minimum volume ellipsoid estimators, the Stahel-Donoho es timator, or other recent proposals) may fail. The use of the procedure is i llustrated through several examples.