A stable sequential multiple test for Koopman–Darmois family

Assuming that data are collected sequentially from multiple streams whose density functions belong to the Koopman–Darmois family, we implement simultaneous testing on multiple hypotheses with respect to parameters. To stabilize the expected sample sizes (ESSs) at all possible values of the true parameters, we intersect individual 2-SPRT plans and propose reasonable thresholds to balance stopping rules among streams. Under two types of constrained familywise error probabilities, we prove that our method has bounded maximum expected sample sizes (MESSs) and achieves asymptotic optimality in the sense of minimizing MESSs. Simulation results demonstrate the stability of our method, in the sense of achieving smaller MESSs than those of the baseline methods. We further apply our method to a real data set.