B1547
Title: Local permutation tests for conditional independence
Authors: Ilmun Kim - Yonsei University (Korea, South) [presenting]
Matey Neykov - Northwestern (United States)
Sivaraman Balakrishnan - Carnegie Mellon University (United States)
Larry Wasserman - Carnegie Mellon University (United States)
Abstract: Local permutation tests are discussed for testing the conditional independence between two random vectors X and Y given Z. The local permutation test determines the significance of a test statistic by locally shuffling samples which share similar values of the conditioning variable Z, and it forms a natural extension of the usual permutation approach for unconditional independence testing. Despite its simplicity and empirical support, the theoretical underpinnings of the local permutation test remain unclear. Motivated by this gap, the aim is to establish theoretical foundations of local permutation tests, focusing on binning-based statistics. Certain classes of smooth distributions are concentrated on and provably tight conditions are identified under which the local permutation method is universally valid, i.e., valid when applied to any (binning-based) test statistic. To complement this result on type I error control, it is also shown that in some cases, a binning-based statistic calibrated via the local permutation method can achieve minimax optimal power.
