Statistics Papers

Document Type

Journal Article

Date of this Version

1981

Publication Source

The Annals of Statistics

Volume

9

Issue

4

Start Page

834

Last Page

845

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.

Keywords

sequential tests, hypothesis testing, Bayes test, exponential family, stopping times, monotone likelihood ratio

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Date Posted: 27 November 2017

This document has been peer reviewed.