## The Annals of Mathematical Statistics

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

#### 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

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
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