Using Angles to Identify Concentrated Multivariate Outliers

This article describes a procedure for the detection of multivariate outliers 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 outliers appear to form a cluster, separated from the sample. It is shown that it presents good properties for the identification of contaminations on high-dimensional sample spaces and for high contamination levels, including some cases in which methods based on robust estimators (the minimum covariance determinant and minimum volume ellipsoid estimators, the Stahel–Donoho estimator, or other recent proposals) may fail. The use of the procedure is illustrated through several examples.