A comparison of nonparametric methods for multivariate two-sample tests

Comparing two multivariate populations can be challenging when the distributional forms are unknown. In such a situation, parametric test procedures are not appropriate given that they require distributional assumptions. In this context, it may be useful to consider the application of nonparametric tests. Specifically, we investigate the application of NonParametric Combination (NPC) which is characterized by high flexibility in the choice of test statistic and is quite powerful in multivariate scenarios. Moreover, it has the advantage of being able to deal with low sample sizes which is a very common situation in real-world applications. The performance of NPC is compared with another nonparametric method well-known in the literature, namely the (depth-based) M-test. A simulation study is provided for the purposes of comparing the performance of the NPC and the data depth-based test. Finally, both test procedures are applied to a real case study.