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March, 1964 Sequential Tests for the Mean of a Normal Distribution II (Large $t$)
John Breakwell, Herman Chernoff
Ann. Math. Statist. 35(1): 162-173 (March, 1964). DOI: 10.1214/aoms/1177703738


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.


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John Breakwell. Herman Chernoff. "Sequential Tests for the Mean of a Normal Distribution II (Large $t$)." Ann. Math. Statist. 35 (1) 162 - 173, March, 1964.


Published: March, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0202.49801
MathSciNet: MR158456
Digital Object Identifier: 10.1214/aoms/1177703738

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 1 • March, 1964
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