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In many applications, hypothesis testing is based on an asymptoticdistribution of statistics. The aim of this paper is to clarify and extendmultiple correction procedures when the statistics are asymptotically Gaussian.We propose a unified framework to prove their asymptotic behavior which isvalid in the case of highly correlated tests. We focus on correlation testswhere several test statistics are proposed. All these multiple testingprocedures on correlations are shown to control FWER. An extensive simulationstudy on correlation-based graph estimation highlights finite sample behavior,independence on the sparsity of graphs and dependence on the values ofcorrelations. Empirical evaluation of power provides comparisons of theproposed methods. Finally validation of our procedures is proposed on realdataset of rats brain connectivity measured by fMRI. We confirm our theoreticalfindings by applying our procedures on a full null hypotheses with data fromdead rats. Data on alive rats show the performance of the proposed proceduresto correctly identify brain connectivity graphs with controlled errors.

Asymptotic control of FWER under Gaussian assumption: application to correlation tests