Abstract
The strength of randomization tests is that they are exact tests under certain symmetry assumption for distributions. In this paper, we propose a randomization test for the mean vector in high dimensional setting. We give an implementation of the proposed randomization test procedure, which is computationally feasible. So far, the asymptotic behaviors of randomization tests have only been studied in fixed dimension case. We investigate the asymptotic behavior of the proposed randomization test in high dimensional setting. It turns out that even if the symmetry assumption is violated, the proposed randomization test still has correct level asymptotically. The asymptotic power function is also given. Our theoretical and simulation results show that the proposed test has a wide application scope while still has good power behavior.
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