A Distance-Distance Plot for Diagnosing Multivariate Outliers

Abstract

We propose a diagnostic method that can be used whenever multiple outliers are identified by robust estimates for multivariate location and scatter. The main purpose is visualization of the multivariate data to help determine whether the detected outliers (a) form a separate cluster or (b) are isolated or randomly scattered (such as heavy tails compared with Gaussian). We make use of Mahalanobis distances in order to check for separation and to reveal additional aspects of the data structure. The method is especially useful if multivariate structure is not seen in bivariate scatterplots.