Asymptotic permutation tests in general factorial designs

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A paradox from randomization-based causal inference (2014, methodology): “In the permutation test literature, some authors (e.g., Neuhaus, 1993; Janssen, 1997; Chung and Romano, 2013; Pauly, Brunner, and Konietschke, 2015) suggested using the Studentized version of τ̂ , i.e., τ̂ /V̂ 1/2 Neyman, as the test statistic.”
Covariate-adjusted Fisher randomization tests for the average treatment effect (2020, methodology): “Motivated by previous work on using studentized statistics for permutation tests (Janssen 1997; Chung and Romano 2013; Pauly et al. 2015; Wu and Ding 2020), we also examine the associated t-statistics studentized by the classic and robust standard errors, respectively (Eicker 1967; Huber 1967; White”
Randomization Tests for Weak Null Hypotheses in Randomized Experiments (2018, methodology): “he type I error without assuming equal distributions in the two sample problem. Chung and Romano (2013) studied the same phenomenon when the parameter of interest could be more general than the mean. Pauly et al. (2015) and Konietschke et al. (2015) used an equivalent studentized statistic in factor”
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).”