Graph modeling enables to outline efficiently interactions between sensors has recently encountered a growing interest. For example in neurosciences, the graph modeling of interactions between brain regions has shed lights on complex mechanisms such as evolution of diseases or recovery after a coma. A whole range of graphical models have been proposed, using either correlation or partial correlation as a measure of dependence. Most of these methods rely on assumptions on the structure of the estimated graphs: sparsity and conditions on the degree distribution for glasso (Friedman et al. 2008), independence between blocks for Stochastic Block Models (SBM) (Holland et al. 1983). In this paper, we propose to use a multiple testing strategy to avoid making such assumptions. We apply multiple correlation tests by controlling the Family Wise Error Rate (FWER). After showing theoretically that the FWER is asymptotically controlled for any graph structures, we implement our approach using different procedures : Bonferroni (1935) procedure, Sidak procedure (Westfall & Young (1993)), Romano & Wolf (2005) boostrap, Drton & Perlman (2007). Using four different graph structures inspired by real data examples, the control is displayed graphically. Finally, we illustrate on simulations that the power of this approach is dependent on the graph structure.
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