## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 2 (1976), 281-291.

### 2-SPRT'S and The Modified Kiefer-Weiss Problem of Minimizing an Expected Sample Size

#### Abstract

A simple combination of one-sided sequential probability ratio tests, called a 2-SPRT, is shown to approximately minimize the expected sample size at a given point $\theta_0$ among all tests with error probabilities controlled at two other points, $\theta_1$ and $\theta_2$. In the symmetric normal and binomial testing problems, this result applies directly to the Kiefer-Weiss problem of minimizing the maximum over $\theta$ of the expected sample size. Extensive computer calculations for the normal case indicate that 2-SPRT's have efficiencies greater than 99% regardless of the size of the error probabilities. Accurate approximations to the error probabilities and expected sample sizes of these tests are given.

#### Article information

**Source**

Ann. Statist. Volume 4, Number 2 (1976), 281-291.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343407

**Digital Object Identifier**

doi:10.1214/aos/1176343407

**Mathematical Reviews number (MathSciNet)**

MR405750

**Zentralblatt MATH identifier**

0367.62099

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 62F20

**Keywords**

Sequential probability ratio test Bayes solution asymptotic optimality

#### Citation

Lorden, Gary. 2-SPRT'S and The Modified Kiefer-Weiss Problem of Minimizing an Expected Sample Size. Ann. Statist. 4 (1976), no. 2, 281--291. doi:10.1214/aos/1176343407. https://projecteuclid.org/euclid.aos/1176343407