Data Depth-Based Nonparametric Tests for Multivariate Scales

The problem of comparing the scales (dispersions) of multivariate samples has been well investigated in the literature, and several parametric and nonparametric methods are available for it. A notion of data depth is used to measure centrality/outlyingness of a point with respect to given data cloud or distribution. Several depth-based tests are available for testing the scale homogeneity of two or more samples. In this paper, an attempt is made for improving the performance of some of the existing depth-based tests for scale homogeneity. The performance of the proposed tests is explored for various distributions and depth functions and is compared with the rank-based test via simulations. The extensive simulation study shows that the proposed modification improves the performance of these tests and also the proposed tests perform better than the rank-based test. The tests are illustrated with real datasets.