Diagnosing Multivariate Outliers Detected by Robust Estimators

We propose a number of diagnostic methods that can be used whenever multiple outliers are identified by robust estimates for multivariate location and scatter. Their main purpose is visualization of the multivariate data to help determine whether the detected outliers (a) form separate clusters or (b) are isolated or randomly scattered (such as heavy tails compared with Gaussian). We make use of Mahalanobis distances and linear projections, to check for separation and to reveal additional aspects of the data structure. Several real data examples are analyzed, and artificial examples are used to illustrate the diagnostic power of the proposed plots. Code to perform the diagnostics, datasets used as examples in the article and documention are available in the online supplements.