## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 35, Number 1 (1964), 162-173.

### Sequential Tests for the Mean of a Normal Distribution II (Large $t$)

John Breakwell and Herman Chernoff

#### Abstract

Asymptotic expansions are derived for the behavior of the optimal sequential test of whether the unknown drift $\mu$ of a Wiener-Levy process is positive or negative for the case where the process has been observed for a long time. The test is optimal in the sense that it is the Bayes test for the problem where we have an a priori normal distribution of $\mu$, the regret for coming to the wrong conclusion is proportional to $|\mu|$, and the cost of observation is constant per unit time. The Bayes procedure is then compared with the best sequential likelihood ratio test.

#### Article information

**Source**

Ann. Math. Statist., Volume 35, Number 1 (1964), 162-173.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177703738

**Digital Object Identifier**

doi:10.1214/aoms/1177703738

**Mathematical Reviews number (MathSciNet)**

MR158456

**Zentralblatt MATH identifier**

0202.49801

**JSTOR**

links.jstor.org

#### Citation

Breakwell, John; Chernoff, Herman. Sequential Tests for the Mean of a Normal Distribution II (Large $t$). Ann. Math. Statist. 35 (1964), no. 1, 162--173. doi:10.1214/aoms/1177703738. https://projecteuclid.org/euclid.aoms/1177703738