Statistics Papers

Document Type

Journal Article

Date of this Version

1981

Publication Source

The Annals of Statistics

Volume

9

Issue

3

Start Page

678

Last Page

682

DOI

10.1214/aos/1176345473

Abstract

Consider the problem of sequentially testing composite, contiguous hypotheses where the risk function is a linear combination of the probability of error in the terminal decision and the expected sample size. Assume that the common boundary of the closures of the null and the alternative hypothesis is compact. Observations are independent and identically distributed. We study properties of Bayes tests. One property is the exponential boundedness of the stopping time. Another property is continuity of the risk functions. The continuity property is used to establish complete class theorems as opposed to the essentially complete class theorems in Brown, Cohen and Strawderman.

Comments

At the time of publication, author Lawrence Brown was affiliated with Cornell University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

Keywords

sequential tests, hypothesis testing, Bayes test, exponentially bounded stopping times, exponential family

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Date Posted: 27 November 2017

This document has been peer reviewed.