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Randomization testing is a fundamental method in statistics, enablinginferential tasks such as testing for (conditional) independence of randomvariables, constructing confidence intervals in semiparametric location models,and constructing (by inverting a permutation test) model-free predictionintervals via conformal inference. Randomization tests are exactly valid forany sample size, but their use is generally confined to exchangeable data. Yetin many applications, data is routinely collected adaptively via, e.g.,(contextual) bandit and reinforcement learning algorithms or adaptiveexperimental designs. In this paper we present a general framework forrandomization testing on adaptively collected data (despite itsnon-exchangeability) that uses a novel weighted randomization test, for whichwe also present novel computationally tractable resampling algorithms forvarious popular adaptive assignment algorithms, data-generating environments,and types of inferential tasks. Finally, we demonstrate via a range ofsimulations the efficacy of our framework for both testing andconfidence/prediction interval construction.

Randomization Tests for Adaptively Collected Data