|| Asymptotics of Sequential Composite Hypothesis Testing under Probabilistic Constraints
||Jiachun Pan, Yonglong Li, Vincent Y.F. Tan, National University of Singapore, Singapore|
||D1-S3-T3: Sequential Hypothesis Testing
||Monday, 12 July, 22:40 - 23:00
||Monday, 12 July, 23:00 - 23:20
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set $\Gamma$. We would like to design a test to decide which hypothesis is in effect. Under the constraints that the probabilities that the length of the test, a stopping time, exceeds n are bounded by a certain threshold $\epsilon$, we obtain certain fundamental limits on the asymptotic behavior of the sequential test as n tends to infinity. Assuming that $\Gamma$ is a convex and compact set, we obtain the set of all first-order error exponents for the problem. We also prove a strong converse. Additionally, under the assumption that $\Gamma$ is a finite set, we obtain the set of second-order error exponents.