Open Access
July, 1981 Bounded Stopping Times for a Class of Sequential Bayes Tests
R. H. Berk, L. D. Brown, Arthur Cohen
Ann. Statist. 9(4): 834-845 (July, 1981). DOI: 10.1214/aos/1176345523

Abstract

Consider the problem of sequentially testing a null hypothesis vs an alternative hypothesis when the risk function is a linear combination of probability of error in the terminal decision and expected sample size (i.e., constant cost per observation.) Assume that the parameter space is the union of null and alternative, the parameter space is convex, the intersection of null and alternative is empty, and the common boundary of the closures of null and alternative is nonempty and compact. Assume further that observations are drawn from a $p$-dimensional exponential family with an open $p$-dimensional parameter space. Sufficient conditions for Bayes tests to have bounded stopping times are given.

Citation

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R. H. Berk. L. D. Brown. Arthur Cohen. "Bounded Stopping Times for a Class of Sequential Bayes Tests." Ann. Statist. 9 (4) 834 - 845, July, 1981. https://doi.org/10.1214/aos/1176345523

Information

Published: July, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0474.62077
MathSciNet: MR619286
Digital Object Identifier: 10.1214/aos/1176345523

Subjects:
Primary: 62L10
Secondary: 52L15 , 62C10

Keywords: Bayes test , exponential family , Hypothesis testing , monotone likelihood ratio , sequential tests , stopping times

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • July, 1981
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