In this article, we consider the problem of testing two separate families of hypotheses via a generalization of the sequential probability ratio test. In particular, the generalized likelihood ratio statistic is considered and the stopping rule is the first boundary crossing of the generalized likelihood ratio statistic. We show that this sequential test is asymptotically optimal in the sense that it achieves asymptotically the shortest expected sample size as the maximal type I and type II error probabilities tend to zero.
Bibliographical noteFunding Information:
This work is supported in part by NSF SES-1323977, DMS-1308566, NIH R37GM047845, and Army Research Laboratory W911NF-14-1-0020.
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- Boundary crossing
- Generalized likelihood ratio test
- Sequential test
- Testing separate families of hypotheses