Sequential Tests for the Mean of a Normal Distribution II (Large $t$)
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.
Permanent link to this document: http://projecteuclid.org/euclid.aoms/1177703738
Digital Object Identifier: doi:10.1214/aoms/1177703738
Mathematical Reviews number (MathSciNet): MR158456
Zentralblatt MATH identifier: 0202.49801