The Annals of Mathematical Statistics

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

John Breakwell and Herman Chernoff

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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


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