Residual randomization tests are shown to be asymptotically valid under a general group-invariance condition and exact in finite samples under a cluster-similarity condition, extending permutation inference to clustered, heteroskedastic, and two-way clustered errors.
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Asymptotic Validity and Finite-Sample Properties of Approximate Randomization Tests
Residual randomization tests are shown to be asymptotically valid under a general group-invariance condition and exact in finite samples under a cluster-similarity condition, extending permutation inference to clustered, heteroskedastic, and two-way clustered errors.