An asymptotically exact multiple testing procedure under dependence

We propose a simple single-step multiple testing procedure that asymptotically controls the family-wise error rate (FWER) at the desired level exactly under the equicorrelated multivariate Gaussian setup. The method is shown to be asymptotically exact using an explicit plug-in estimator for the equicorrelation, and does not require stepwise adjustments. We establish its theoretical properties, including the convergence to the desired error level (along with an estimate of the rate of convergence), and demonstrate its effectiveness through simulation results. We also spell out related extensions to unknown equicorrelation, block-correlated structures and generalized FWER control.