Tests of mutual independence among several random vectors using univariate and multivariate ranks of nearest neighbours

Testing mutual independence among several random vectors of arbitrary dimensions is a challenging problem in Statistics, and it has gained considerable interest in recent years. In this article, we propose some nonparametric tests based on different notions of ranks of nearest neighbour. These proposed tests can be conveniently used for high dimensional data, even when the dimensions of the random vectors are larger than the sample size. We investigate the performance of these tests on several simulated and real data sets and also use them in identifying causal relationships among the random vectors. Our numerical results show that they can outperform state-of-the-art tests in a wide variety of examples.