  Recently, the binary expansion testing framework was introduced to test the
independence of two continuous random variables by utilizing 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 distance correlation. Simulation studies suggest that this
method improves the power while preserving the clear interpretation of the
binary expansion testing. We extend this method to tests of independence of
random vectors in arbitrary dimension. Through random projections, the proposed
binary expansion randomized ensemble test transforms the multivariate
independence testing problem into a univariate problem. Simulation studies and
data example analyses show that the proposed method provides relatively robust
performance compared with existing methods.
