## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 1 (1977), 1-21.

### Nearly-Optimal Sequential Tests for Finitely Many Parameter Values

#### Abstract

Combinations of one-sided sequential probability ratio tests (SPRT's) are shown to be "nearly optimal" for problems involving a finite number of possible underlying distributions. Subject to error probability constraints, expected sample sizes (or weighted averages of them) are minimized to within $o(1)$ asymptotically. For sequential decision problems, simple explicit procedures are proposed which "do exactly what a Bayes solution would do" with probability approaching one as the cost per observation, $c$, goes to zero. Exact computations for a binomial testing problem show that efficiencies of about 97${\tt\%}$ are obtained in some "small-sample" cases.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 1 (1977), 1-21.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343737

**Digital Object Identifier**

doi:10.1214/aos/1176343737

**Mathematical Reviews number (MathSciNet)**

MR438610

**Zentralblatt MATH identifier**

0386.62070

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 62F20

**Keywords**

Sequential probability ratio test Bayes solution asymptotic optimality

#### Citation

Lorden, Gary. Nearly-Optimal Sequential Tests for Finitely Many Parameter Values. Ann. Statist. 5 (1977), no. 1, 1--21. doi:10.1214/aos/1176343737. https://projecteuclid.org/euclid.aos/1176343737