Multivariate Nonparametric Test of Independence

The problem of testing mutual independence of $p$ random vectors in a general setting where the dimensions of the vectors can be different and the distributions can be discrete, continuous or both is of great importance. We propose such a test which utilizes multivariate characteristic functions and is a generalization of known results. We characterize the limiting distribution of the test statistic under the null hypothesis. The limiting null distribution is approximated and the method is validated. Numerical results based on simulations are investigated and our methodology is implemented in the $\texttt{R}$ package $\texttt{IndependenceTests}$. Power comparisons are also presented for some partial cases of our general test, where some competitive procedures exist.