Minimax optimality of permutation tests

Understand

Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement.

• Despite its increasing popularity and empirical success, theoretical properties of the permutation test, especially its power, have not been fully explored beyond simple cases.
• In this paper, we attempt to partly fill this gap by presenting a general non-asymptotic framework for analyzing the minimax power of the permutation test.
• The utility of our proposed framework is illustrated in the context of two-sample and independence testing under both discrete and continuous settings.