The Binary Expansion Randomized Ensemble Test (BERET)

Abstract

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 by an ensemble method 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. By 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.

BEAUTY Powered BEAST

“…Although the test based on Spearman's ρ has a higher power against the linear form of dependency particularly present in bivariate normal distributions, we see from (Ma and Mao, 2019). Multivariate extensions of these methods include Gorsky and Ma (2018); Lee et al (2019).…”

“…The theory and methods are similar as shown in Zhang (2019). Recent nonparametric tests of independence include Hoeffding (1948); Miller and Siegmund (1982);Székely et al (2007); Gretton et al (2007); Reshef et al (2011); Zheng et al (2012); Heller et al (2013); Sejdinovic et al (2014); Kinney and Atwal (2014); ; Pfister et al (2016); ; Zhu et al (2017); Jin and Matteson (2018); Ma and Mao (2019); Lee et al (2019); Cao and Bickel (2020); Shi et al (2020); Chatterjee (2020); Geenens and de Micheaux (2020), and references therein.…”

Comments on: A Gibbs sampler for a class of random convex polytopes

“…One general approach in nonparametric tests of independence is the multi-resolution approach. See some recent work by Ma and Mao (2019); Zhang (2019); Lee et al (2019); Gorsky and Ma (2018); Zhang et al (2021). Some advantages of this approach include uniform consistency, minimax optimal power, clear interpretability and efficient computation.…”