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July, 1973 Optimal Stopping and Sequential Tests which Minimize the Maximum Expected Sample Size
Tze Leung Lai
Ann. Statist. 1(4): 659-673 (July, 1973). DOI: 10.1214/aos/1176342461


Among all sequential tests with prescribed error probabilities of the null hypothesis $H_0: \theta = -\theta_1$ versus the simple alternative $H_1: \theta = \theta_1$, where $\theta$ is the unknown mean of a normal population, we want to find the test which minimizes the maximum expected sample size. In this paper, we formulate the problem as an optimal stopping problem and find an optimal stopping rule. The analogous problem in continuous time is also studied, where we want to test whether the drift coefficient of a Wiener process is $-\theta_1$ or $\theta_1$. By reducing the corresponding optimal stopping problem to a free boundary problem, we obtain upper and lower bounds as well as the asymptotic behavior of the stopping boundaries.


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Tze Leung Lai. "Optimal Stopping and Sequential Tests which Minimize the Maximum Expected Sample Size." Ann. Statist. 1 (4) 659 - 673, July, 1973.


Published: July, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0261.62062
MathSciNet: MR426317
Digital Object Identifier: 10.1214/aos/1176342461

Keywords: 6062 , 6225 , 6245 , Brownian motion , continuation region , free boundary problem , Generalized sequential probability ratio test , Harmonic function , least excessive majorant , optimal stopping rule , space-time process , symmetric test

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 4 • July, 1973
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