Large‐scale simultaneous inference under dependence

Simultaneous inference allows for the exploration of data while deciding on criteria proclaiming discoveries. It was recently proved that all admissible post hoc methods true discoveries must employ closed testing. In this paper, we investigate efficient testing with local tests a special form: thresholding function sums test scores individual hypotheses. Under design, propose new statistic quantifies cost multiplicity adjustments, and develop fast (mostly linear-time) algorithms inference. Paired recent advances in global null based generalized means, our work instantiates series simultaneous can handle many dependence structures signal compositions. We provide guidance method choices via theoretical investigation conservativeness sensitivity different tests, as well simulations find analogous behavior full