## The Annals of Statistics

- Ann. Statist.
- Volume 6, Number 4 (1978), 910-916.

### Optimality and Almost Optimality of Mixture Stopping Rules

#### Abstract

It is shown that for a test of a composite hypothesis on the parameter $\theta$ of an exponential family of distributions, mixture stopping rules are almost optimal with respect to certain criteria of optimality and a unique stopping rule is to be found among them which is optimal with respect to another type of optimality.

#### Article information

**Source**

Ann. Statist. Volume 6, Number 4 (1978), 910-916.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176344264

**Digital Object Identifier**

doi:10.1214/aos/1176344264

**Mathematical Reviews number (MathSciNet)**

MR494737

**Zentralblatt MATH identifier**

0378.62071

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62L05: Sequential design

**Keywords**

Optimality mixture stopping rules open ended tests ASN minimax Bayes optimal stopping exponential family Brownian motion

#### Citation

Pollak, Moshe. Optimality and Almost Optimality of Mixture Stopping Rules. Ann. Statist. 6 (1978), no. 4, 910--916. doi:10.1214/aos/1176344264. http://projecteuclid.org/euclid.aos/1176344264.