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

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Abstract
This work proposes innovative permutation-based procedures controlling the familywise error rate (FWE). It is proved that weighted procedures control the FWE if weights are a function of the sufficient statistic. We particularly focus on the use of additional information given by the total variance of each variable. 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 is shown, and a comparative simulation study highlights its usefulness even in experimental situations with a high number of elementary hypotheses.