Generalized Sequential Probability Ratio Test for Separate Families of Hypotheses

Xiaoou Li, Jingchen Liu, Zhiliang Ying

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)539-563
Number of pages25
JournalSequential Analysis
Issue number4
StatePublished - Oct 25 2014

Bibliographical note

Funding Information:
This work is supported in part by NSF SES-1323977, DMS-1308566, NIH R37GM047845, and Army Research Laboratory W911NF-14-1-0020.

Publisher Copyright:
© 2014, Copyright Taylor & Francis Group, LLC.


  • Boundary crossing
  • Generalized likelihood ratio test
  • Sequential test
  • Testing separate families of hypotheses


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