A1230
Title: Correlation comparison after nonlinear transformations
Authors: Elio Zhang - Seattle University (United States) [presenting]
Abstract: Testing the equality of two or more correlation matrices is a fundamental problem in many scientific fields, especially when the number of variables is large relative to the sample size. Recent work has shown empirically that coupling entrywise transformations with permutation can substantially improve power in such settings, yet the mechanism behind these gains and principled guidance for choosing transformations remain unclear. These gaps are addressed through two contributions. First, a theoretical explanation is provided of why and how entrywise transformations, when paired with a permutation (random-partition) calibration, can elevate power: the transformation reshapes and amplifies distributional discrepancies across matrix entries while the permutation procedure preserves valid type-I error control under the null. Second, and more importantly, a power-driven criterion is developed for selecting (within a broad class of smooth transformations) an optimal transformation that maximizes asymptotic power without inflating type-I error. The optimality of the proposed choice is established both theoretically and via extensive simulations, and the practical utility of the method is demonstrated through analyses of two real data examples.
