Suitable sequentially rejective multiple test procedures allow to “zoom in" on clusters of relevant variables in high-dimensional regression (Meinshausen ), or on regions of interest in some search space (Heinrich et al. ; Meinshausen et al. ). As a common framework for these schemes we propose to consider multiple testing along a tree of hypotheses together with a “keep rejecting until first acceptance" rule. Particular topics addressed in this note are control of the familywise error, and some variants and basic properties of the procedure.
"Multiple testing along a tree." Electron. J. Statist. 4 461 - 471, 2010. https://doi.org/10.1214/09-EJS496