## The Annals of Statistics

- Ann. Statist.
- Volume 8, Number 5 (1980), 1110-1122.

### Risk of Asymptotically Optimum Sequential Tests

#### Abstract

The problem considered is that of testing sequentially between two separated composite hypotheses concerning the mean of a normal distribution with known variance. The parameter space is the real line, on which is assumed an a priori distribution, $W,$ with full support. A family $\{\delta(c)\}$ of sequential tests is defined and shown to be asymptotically Bayes, as the cost, $c$, per observation tends to zero, relative to a large class of fully supported a priori distributions. The ratio of the integrated risk of the Bayes procedure to that of $\delta(c)$ is shown to be $1 - 0(\log\log c^{-1}/\log c^{-1})$, as $c$ tends to zero, for every $W.$

#### Article information

**Source**

Ann. Statist., Volume 8, Number 5 (1980), 1110-1122.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345148

**Digital Object Identifier**

doi:10.1214/aos/1176345148

**Mathematical Reviews number (MathSciNet)**

MR585709

**Zentralblatt MATH identifier**

0452.62068

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 62F05: Asymptotic properties of tests

**Keywords**

Integrated risk asymptotically Bayes sequential tests asymptotic efficiency

#### Citation

Zerdy, Gloria C. Risk of Asymptotically Optimum Sequential Tests. Ann. Statist. 8 (1980), no. 5, 1110--1122. doi:10.1214/aos/1176345148. https://projecteuclid.org/euclid.aos/1176345148