A test based on data depth for testing location-scale of the two multivariate populations

In the present article, a two-sample test for testing location and/or scale parameter of two multivariate populations is proposed. Baumgartner et al. [A nonparametric test for the general two-sample problem. Biometrics. 1998:1129–1135] proposed a univariate rank test for a general alternative. Murakami [Modified Baumgartner statistics for the two-sample and multisample problems: a numerical comparison. J Stat Comput Simul. 2012;82(5):711–728] modified this univariate rank test with the help of expectations and variances of ordered ranks. With the help of these tests, we have proposed a new rank test for testing location and/or scale parameters of two multivariate populations. Concept of data depth and permutation test are used to define the test procedure. The proposed test is compared with the existing tests for testing location and/or scale parameters of two multivariate populations by using extensive simulated size and power study. The simulation study reveals that the proposed test outperforms the existing tests for majority of the cases. The test procedure is illustrated with well-known Turtles data.