The Binary Expansion Randomized Ensemble Test (BERET)
This work addresses independence testing in statistics, offering a method that is incremental but extends applicability to multivariate data with improved robustness.
The authors tackled the problem of testing independence between continuous random variables and random vectors by developing the Binary Expansion Randomized Ensemble Test (BERET), which improved power while preserving interpretability and extended to multivariate cases via random projections, showing robust performance in simulations and data analyses.
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.