Depth-based graphical tools and related tests for multivariate multi-sample problems

A notion of data depth is used to measure the centrality/outlyingness of a given point with respect to a given distribution or data cloud. Several depth-based graphical tools and nonparametric tests have been proposed for the comparison of two or more multivariate distributions. This article proposes graphical tools for the comparison of multiple multivariate distributions. These graphical tools can be considered as a generalization of the well-known depth versus depth plot (DD-plot) for the visual comparison of the two multivariate samples. Different types of variations in location, scale, skewness, or kurtosis among distributions give rise to different deviation patterns in the proposed plots. Based on these graphical tools we generalize the statistical tests for two sample location, scale, and homogeneity of species assemblages to the corresponding multi-sample problems. An extensive simulation study reveals that the performances of the proposed tests are superior to that of the existing tests. The proposed graphical tools and tests are illustrated with different simulated and real data sets.