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The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that the statistics are asymptotically normal under the weak requirement that the target parameter can be consistently estimated at the parametric rate. This holds for regular estimators under many well\u2010known forms of weak dependence and justifies the claim of dependence robustness. We consider applications to settings with unknown or complicated forms of dependence, with various forms of network dependence as leading examples. 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