Testing for independence of sets of high-dimensional normal vectors using random projection approach

A simple test is proposed to test the independence of high-dimensional random normal vectors. The method consists of two steps. First, the primary high-dimensional data is projected onto a low-dimensional subspace multiple times using random projection matrices. Second, the test statistic is constructed by utilizing the classical statistics obtained from the projected low-dimensional datasets. Simulations are performed to compare the performance of the proposed test with existing state-of-the-art tests, in terms of test sizes and powers. Finally, the proposed methodology is illustrated using two gene datasets, namely the Colon and Leukemia cancer datasets.