Nonparametric depth-based multivariate outlier identifiers, and robustness properties

DMS-0103698 and CCF-0430366 is gratefully acknowledged. In extending univariate outlier detection methods to higher dimension, various special issues arise, such as limitations of visualization methods, inadequacy of marginal methods, lack of a natural order, limited scope of parametric modeling, and restriction to ellipsoidal contours when using Mahalanobis distance methods. Here we pass beyond these limitations via an approach based on depth functions, which order multidimensional data points by “outlyingness ” measures and generate contours following the shape of the data set. This approach to multivariate outlier detection is nonparametric and, with typical choices of depth function, robust. For depth-based outlier identifiers, we define masking and swamping breakdown points, adapting ideas of Davie