Sequential Multiple Testing with Three Hypotheses and Known Number of Streams Following Each Hypothesis

In this work, we consider the problem of testing the marginal distributions of multiple independent, sequentially observed data streams, where for each stream there are three hypotheses to select from. We assume that the exact number of streams following each hypothesis is a priori known. The goal is to devise a sequential multiple testing procedure that (i) controls the familywise error probabilities of all types below arbitrary user-specified levels, and (ii) achieves the minimum expected sample size under all possible distributions and among all testing procedures that control the error probabilities below the same levels, asymptotically as the levels go to zero. The extension to arbitrary number of hypotheses and arbitrary form of prior information is set as future directions. A preprint version is available at https://doi.org/10.13140/RG.2.2.14922.43209.