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Paper IDE.6.3
Paper Title Second-Order Asymptotics of Sequential Hypothesis Testing
Authors Yonglong Li, Vincent, Y. F. Tan, National University of Singapore, Singapore
Session E.6: Hypothesis Testing II
Presentation Lecture
Track Detection and Estimation
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions P 0 and P 1 and we would like to decide which hypothesis is true using a sequential test. It is known from the work of Wald and Wolfowitz that as the expectation of the length of the test grows, the optimal typeI and type-II error exponents approach the relative entropies D(P 1 ∥ P 0 ) and D(P 0 ∥ P 1 ). We refine this result by considering the optimal backoff from the corner point of the achievable exponent region (D(P 1 ∥ P 0 ), D(P 0 ∥ P 1 )) under the expectation constraint on the length of the test (or the sample size). We consider the expectation constraint in which the expectation of the sample size is bounded by n, and under mild conditions, characterize the backoff, also coined second-order asymptotics, precisely. Examples are provided to illustrate our results.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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