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

John Breakwell and Herman Chernoff
Source: Ann. Math. Statist. Volume 35, Number 1 (1964), 162-173.

#### 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.

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