A necessary test for complete independence in high dimensions using rank-correlations

We propose a nonparametric necessary test for the complete independence of random variables in high-dimensional environment. The test is constructed based on Spearman’s rank-correlations and is shown to be asymptotically normal by the martingale central limit theorem as both the sample size and the dimension of variables go to infinity. Simulation studies show that the proposed test works well in finite-sample situations.