Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation
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. AMS 2000 subject classifications: 62G10, 62J15, 62L99.