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Activity Number: 407
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #305405
Title: Almost Minimax Open-Ended Mixture-Based Sequential Tests
Author(s): Georgios Fellouris*+ and Alexander G. Tartakovsky
Companies: University of Southern California and University of Southern California
Address: 3620 S. Vermont Ave, Los Angeles, CA, 90089-2532,
Keywords: Mixture rules ; Minimax tests ; Open-ended tests ; Asymptotic Optimality ; Sequential testing ; Tests of power one

We consider the problem of sequentially testing a simple null hypothesis against a composite alternative hypothesis. The goal is to find a sequential scheme (i.e. a stopping rule) that stops as soon as possible under any state of the alternative, while controlling the probability of a false alarm (i.e. stopping under the null). The main result that will be presented is the design of a mixture-based stopping rule that is almost minimax in an appropriate sense. This is achieved when the alternative hypothesis is discrete, as well as when it consists of a continuum of probability measures which belong to an exponential family. The proof relies on the discovery of an almost Bayes rule for an appropriate sequential decision problem and on asymptotic approximations for the operating characteristics of arbitrary mixture-based sequential tests, which are obtained using non-linear renewal theory. The optimal mixing distribution depends on renewal-theoretic quantities, which can be easily computed. We use simulation experiments to verify the accuracy of our asymptotic approximations and evaluate the performance of alternative mixture-based stopping rules.

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