High-Dimensional Sequential Testing of Multiple Hypotheses

Yiming Xing, Shen Yan, Ziming Wang

Abstract: The problem of simultaneously testing the distributions of a large number of independent, sequentially observed data streams is considered, where the same multiple hypotheses are posed for each data stream, and the goal is to correctly identify all data streams following each hypothesis. A decentralized setup is adopted, under which the testing procedure applied to each data stream must be the same and can only use local observations. A novel criterion of high-dimensional asymptotic optimality is proposed, according to which the goal is to achieve the optimal expected average sample size, uniformly in all possible hypothesis configurations, asymptotically as the total number of data streams and the maximum possible numbers of data streams following each hypothesis go to infinity, in the class of all testing procedures that control the same levels of familywise error rates. We show that this criterion is achieved by the multihypothesis sequential probability ratio test.