title: Generalized Sequential Probability Ratio Test for Separate Families of Hypotheses.
abstract: In this paper, 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.
authors.affiliation: Department of Statistics, Columbia University, New York, NY 10027, USA.
authors.forename: Xiaoou
authors.initials: X
authors.lastname: Li
authors.affiliation: Department of Statistics, Columbia University, New York, NY 10027, USA.
authors.forename: Jingchen
authors.initials: J
authors.lastname: Liu
authors.affiliation: Department of Statistics, Columbia University, New York, NY 10027, USA.
authors.forename: Zhiliang
authors.initials: Z
authors.lastname: Ying
keywords: boundary crossing; generalized likelihood ratio test; sequential test; testing separate families of hypotheses