Adaptive Geo-Topological Independence Criterion
This work addresses a fundamental statistical challenge for researchers and practitioners needing robust dependence tests, though it appears incremental as it builds on existing methods like distance correlation.
The paper tackles the problem of testing statistical dependence between variables by introducing adaptive independence criteria based on nonlinear transformations of distances, which empirically outperform established tests in average and worst-case sensitivity across various relationships.
Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the variables, promising robust power across scenarios. Building on the distance correlation, we introduce a family of adaptive independence criteria based on nonlinear monotonic transformations of distances. We show that these criteria, like the distance correlation and RKHS-based criteria, provide dependence indicators. We propose a class of adaptive (multi-threshold) test statistics, which form the basis for permutation tests. These tests empirically outperform some of the established tests in average and worst-case statistical sensitivity across a range of univariate and multivariate relationships, offer useful insights to the data and may deserve further exploration.