Testing independence in high-dimensional multivariate normal data

Abstract

A simple statistic was proposed for testing the complete independence of components of random vector having a multivariate normal distribution. Using the martingale central limit theorem, it was proved that this test statistic converges in distribution to the normal as long as both the sample size and dimension go to infinity. Simulations were also carried out to performance evaluation of the proposed test for dealing with the high-dimensional data and the results were compared to those of the state-of-the-art tests. The results confirmed that, in terms of the average relative error criterion, the proposed test has adequate type I error rate control and comparable power to those tests with smaller size distortions.