Testing for Independence with BERET

• Activity Number: 288 - New Insights from Classical Wisdom—honoring Lawrence D. Brown’s Contributions to Graduate Student Education
• Type: Topic Contributed
• Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Duyeol Lee* and Kai Zhang and Michael Kosorok
• Companies: University of North Carolina at Chapel Hill and University of North Carolina, Chapel Hill and University of North Carolina at Chapel Hill
• Keywords: Independence test; Nonparametric inference; Binary Expansion; Multivariate

Abstract

Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics which are complete sufficient statistics for dependence. In this paper, we develop a new test through an ensemble method utilizing both the sum of squared symmetry statistics and distance correlation. Simulation studies suggest that the proposed method improves the power while preserving the clear interpretation of the binary expansion testing. We further extend this method to tests of independence of random vectors in arbitrary dimension. The proposed binary expansion randomized ensemble test (BERET) transforms the multivariate independence testing problem into a univariate one through random projections. The power of the proposed method is illustrated with many simulated and real data examples.