## The Annals of Statistics

- Ann. Statist.
- Volume 9, Number 3 (1981), 678-682.

### Properties of Bayes Sequential Tests

R. H. Berk, L. D. Brown, and Arthur Cohen

#### 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.

#### Article information

**Source**

Ann. Statist., Volume 9, Number 3 (1981), 678-682.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345473

**Digital Object Identifier**

doi:10.1214/aos/1176345473

**Mathematical Reviews number (MathSciNet)**

MR615445

**Zentralblatt MATH identifier**

0478.62066

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62L15: Optimal stopping [See also 60G40, 91A60]

**Keywords**

Sequential tests hypothesis testing Bayes test exponentially bounded stopping times exponential family

#### Citation

Berk, R. H.; Brown, L. D.; Cohen, Arthur. Properties of Bayes Sequential Tests. Ann. Statist. 9 (1981), no. 3, 678--682. doi:10.1214/aos/1176345473. https://projecteuclid.org/euclid.aos/1176345473