A multivariate control quantile test using data depth

The objective of this article is to present a depth based multivariate control quantile test using statistically equivalent blocks (DSEBS). Given a random sample {x1,…,xm} of Rd-valued random vectors (d≥1) with a distribution function (DF) F, statistically equivalent blocks (SEBS), a multivariate generalization of the univariate sample spacings, can be constructed using a sequence of cutting functions hi(x) to order xi,i=1,…,m. DSEBS are data driven, center-outward layers of shells whose shapes reflect the underlying geometric features of the unknown distribution and provide a framework for selection and comparison of cutting functions. We propose a control quantile test, using DSEBS, to test the equality of two DFs in Rd. The proposed test is distribution free under the null hypothesis and well defined when d≥max(m,n). A simulation study compares the proposed statistic to depth-based Wilcoxon rank sum test. We show that the new test is powerful in detecting the differences in location, scale and shape (skewness or kurtosis) changes in two multivariate distributions.