Some Non - Asymptotic Results on Resampling in High Dimension , Ii : Multiple Tests

In the context of correlated multiple tests, we aim at controlling non-asymptotically the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one and two-sided multiple testing problem for the mean values of its coordinates. We address this problem by using the confidence regions developed in the companion paper [1], which lead directly to single-step procedures; these can then be improved using step-down algorithms, following an established general methodology laid down by Romano and Wolf [16]. We compare the performance of the different obtained thresholds on simulated data.