A0767
Title: Sequential multiple testing: An overview of different setups
Authors: Yiming Xing - University of Illinois at Urbana-Champaign (China) [presenting]
Abstract: The problem of simultaneously testing the marginal distributions of sequentially monitored data streams is considered. To solve this problem, the need is to specify, for each data stream, a time for making a decision, a time for stopping sampling, and a decision rule. Based on whether information could be shared among data streams, there are the decentralized setup and the centralized setup, and based on the relationship between the times of making a decision and the times of stopping sampling, the centralized setup could be further divided into the synchronous setup, the asynchronous-decision setup, the asynchronous-stopping setup, and other setups. An overview of all these setups is given, and one solution for the asynchronous-decision setup is elaborated. Specifically, a novel sequential multiple testing procedure is proposed, which minimizes the expected sample size in every data stream under every possible hypothesis configuration, asymptotically as certain global error metrics go to zero. This asymptotic optimality result is established under general parametric composite hypotheses, various error metrics, and weak distributional assumptions that allow for temporal dependence.
