## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 5 (1977), 866-880.

### Power-One Tests Based on Sample Sums

#### Abstract

This paper studies the properties of open-ended power-one tests of $H_0: \theta \leqq \theta_0$ versus $H_1: \theta > \theta_0$ or of $H: \theta = \theta_0$ versus $K: \theta \neq \theta_0$ based on sample sums stopped at moving boundaries. The behavior of the expected sample size is analyzed and certain asymptotic results as $\theta \rightarrow \theta_0$ are obtained in the case of a location parameter and also in the case of an exponential family of distributions.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 5 (1977), 866-880.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343943

**Digital Object Identifier**

doi:10.1214/aos/1176343943

**Mathematical Reviews number (MathSciNet)**

MR488545

**Zentralblatt MATH identifier**

0368.62011

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F05: Asymptotic properties of tests

Secondary: 62L10: Sequential analysis 60F99: None of the above, but in this section

**Keywords**

Power-one tests expected sample size location parameter exponential family first passage problems

#### Citation

Lai, Tze Leung. Power-One Tests Based on Sample Sums. Ann. Statist. 5 (1977), no. 5, 866--880. doi:10.1214/aos/1176343943. https://projecteuclid.org/euclid.aos/1176343943