Multivariate and multiple permutation tests

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Controlling the false discovery rate via knockoffs (2014, background): “While they may be quite effective under a global null, they may fail to yield correct answers in cases other than the global null; see also [6, 7] for other sources of problems associated with permutation methods.”
Randomization Tests for Weak Null Hypotheses in Randomized Experiments (2018, background): “Under iid sampling and vector potential outcomes, Chung and Romano (2016) addressed the two-sample problem with permutation tests.”
Minimax optimality of permutation tests (2020, background): “Finally, we also note that the robustness of permutation tests to violations of the exchangeability condition has been investigated by Romano (1990); Chung and Romano (2013); Pauly et al. (2015); Chung and Romano (2016); DiCiccio and Romano (2017).”