Asymptotically valid and exact permutation tests based on two-sample U-statistics

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Multivariate and multiple permutation tests (2016, methodology): “However, this reduces the problem to the mean case in However, contiguity results between multinomial and multivariate hypergeometric distributions (see Lemma 3.3 of Chung and Romano (2011)) guarantee both (61) and (62).”
Bias-Reduced Doubly Robust Estimation (2015, background): “Chung and Romano (2011, 2013) show that a permutation test based on the Mann-Whitney statistic which is appropriately studentized by a consistent estimator for its unconditional variance, achieves the correct asymptotic Type I error under the weak null hypothesis P(Y Y ∗|A = 0,A∗= 1) = 0.5 (or more ”
Covariate-adjusted Fisher randomization tests for the average treatment effect (2020, methodology): “Rerandomization, termed by Cox (1982) and Morgan and Rubin (2012), samples the treatment indicators under covariate balance constraints.”
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.”