Data depth and its induced center-outward ordering have given rise to many useful tools in nonparametric multivariate analysis. A DD-plot (depth vs depth plot) is the two dimensional scatter plot of depth values of the given sample points with respect to the two underlying distributions. It can be a useful tool to visualize the difference of two distributions. We discuss some of the utilities of DD-plots in this presentation. In particular, we discuss approaches devised from DD-plots to classification (thus named DD classifier) and testing the difference between two samples. The approaches are completely data driven and the classification or test outcomes can be easily visualized on

the two-dimensional DD-plot regardless how high the dimension of the data. Moreover, these approaches are easy to implement and they bypasses the task of estimating underlying parameters such as means and scales, often required by the existing statistical approaches.  We show that DD-classifier is asymptotically equivalent to the Bayes rule under suitable conditions, and it can achieve Bayes error for a family broader than elliptical distributions. Overall, DD-classifier performs well across a broad range of settings, and compares favorably with existing methods, including KNN and SVM. It can also be robust against outliers or contamination.

This is joint work with Juan Cuesta-Albertos (Universidad de Cantabria, Spain) and Jun Li (University of California, Riverside).