Weighted methods controlling the FWE when the number of variables is much higher than the number of observations

This work proposes innovative permutation-based procedures controlling the Familywise Error rate (FWE). It is proofed that weighted procedures control the FWE if weights are a function of the sufficient statistic. Particularly, we focus on the use of the additional information given by the total variance of each variables. The first proposal considers the use of weights applied to the combining functions of the Closed Testing procedure; the second proposal exploits this information to identify clusters upon which to apply a “Sequential Gatekeeping” procedure. An application to real data