Signal Recovery with Multistage Tests and without Sparsity Constraints

A signal recovery problem is considered, where the same binary testing posed over multiple, independent data streams. The goal to identify all signals (resp. noises), i.e., streams alternative null) hypothesis correct, subject prescribed bounds on classical or generalized familywise error probabilities of both types. It not required that exact number be a priori known, only upper numbers and noises are assumed instead. decentralized formulation adopted, according which sample size decision for each must based observations from corresponding stream. novel multistage procedure proposed this shown enjoy high-dimensional asymptotic optimality property. Specifically, it achieves optimal, average streams, expected size, uniformly in true signals, as maximum possible go infinity at arbitrary rates, class sequential tests with global control. In contrast, existing literature achieve property under additional sparsity symmetry conditions. These results an analysis fundamental two zero. Moreover, they supported by simulation studies extended problems non-iid composite hypotheses.