The Annals of Statistics

Sequential Detection of a Change in a Normal Mean when the Initial Value is Unknown

Moshe Pollak and D. Siegmund

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 19, Number 1 (1991), 394-416.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347990

Digital Object Identifier
doi:10.1214/aos/1176347990

Mathematical Reviews number (MathSciNet)
MR1091859

Zentralblatt MATH identifier
0732.62080

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis
Secondary: 62N10

Keywords
Change-point problem sequential detection

Citation

Pollak, Moshe; Siegmund, D. Sequential Detection of a Change in a Normal Mean when the Initial Value is Unknown. Ann. Statist. 19 (1991), no. 1, 394--416. doi:10.1214/aos/1176347990. https://projecteuclid.org/euclid.aos/1176347990


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