## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 5 (1976), 891-911.

### Asymptotic Efficiencies of Sequential Tests

#### Abstract

Some concepts of relative and absolute efficiency for sequential tests are considered. These are sequential analogs of Hodges-Lehmann and Chernoff efficiencies. Using these criteria, several sequential tests for the mean of a normal distribution are evaluated. Among them are Wald's SPRT, Anderson's triangular boundary, Bayes and APO tests and a repeated significance test. Truncated versions of these tests are also considered. Asymptotic expressions for the (expected) stopping times and error rates are given.

#### Article information

**Source**

Ann. Statist., Volume 4, Number 5 (1976), 891-911.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343587

**Digital Object Identifier**

doi:10.1214/aos/1176343587

**Mathematical Reviews number (MathSciNet)**

MR418368

**Zentralblatt MATH identifier**

0374.62076

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 62F05: Asymptotic properties of tests 62F20 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62E20: Asymptotic distribution theory

**Keywords**

Sequential test asymptotic efficiency SPRT truncated sequential test Anderson's boundaries APO test Bayes sequential test repeated significance test Wiener process

#### Citation

Berk, Robert H. Asymptotic Efficiencies of Sequential Tests. Ann. Statist. 4 (1976), no. 5, 891--911. doi:10.1214/aos/1176343587. https://projecteuclid.org/euclid.aos/1176343587