Open Access
March, 1991 Sequential Detection of a Change in a Normal Mean when the Initial Value is Unknown
Moshe Pollak, D. Siegmund
Ann. Statist. 19(1): 394-416 (March, 1991). DOI: 10.1214/aos/1176347990


Three stopping rules are proposed to detect a change in a normal mean, when the initial value of the mean is unknown but an estimate obtained from a training sample is available. Asymptotic approximations are given for the average run length when there is no change. Under certain hypotheses about the length of time before the change occurs and the magnitude of the change, we obtain asymptotic approximations for the expected delay in detection in terms of the corresponding expected delay in the much simpler case of a known initial value. The results of a Monte Carlo experiment supplement our asymptotic theory to yield some general conclusions about the relative merits of the three stopping rules and guidelines for choosing the size of the training sample.


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Moshe Pollak. D. Siegmund. "Sequential Detection of a Change in a Normal Mean when the Initial Value is Unknown." Ann. Statist. 19 (1) 394 - 416, March, 1991.


Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0732.62080
MathSciNet: MR1091859
Digital Object Identifier: 10.1214/aos/1176347990

Primary: 62L10
Secondary: 62N10

Keywords: Change-point problem , sequential detection

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • March, 1991
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