Abstract: The binary expansion testing framework was recently introduced to test the independence of two continuous random variables by using symmetry statistics that are complete sufficient statistics for dependence. We develop a new test based on an ensemble approach that uses the sum of squared symmetry statistics and the distance correlation. Simulation studies suggest that this method has improved power, while preserving the clear interpretation of the binary expansion testing. We extend this method to tests of independence of random vectors in an arbitrary dimension. Using random projections, the proposed binary expansion randomized ensemble test transforms the multivariate independence testing problem into a univariate problem. Simulation studies and data examples show that the proposed method provides relatively robust performance compared with that of existing methods.

Keywords words and phrases: Binary Expansion, monparametric inference, multiple testing, multivariate analysis, nonparametric test of independence.