The Annals of Statistics

Sequential multi-sensor change-point detection

Yao Xie and David Siegmund

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Abstract

We develop a mixture procedure to monitor parallel streams of data for a change-point that affects only a subset of them, without assuming a spatial structure relating the data streams to one another. Observations are assumed initially to be independent standard normal random variables. After a change-point the observations in a subset of the streams of data have nonzero mean values. The subset and the post-change means are unknown. The procedure we study uses stream specific generalized likelihood ratio statistics, which are combined to form an overall detection statistic in a mixture model that hypothesizes an assumed fraction $p_{0}$ of affected data streams. An analytic expression is obtained for the average run length (ARL) when there is no change and is shown by simulations to be very accurate. Similarly, an approximation for the expected detection delay (EDD) after a change-point is also obtained. Numerical examples are given to compare the suggested procedure to other procedures for unstructured problems and in one case where the problem is assumed to have a well-defined geometric structure. Finally we discuss sensitivity of the procedure to the assumed value of $p_{0}$ and suggest a generalization.

Article information

Source
Ann. Statist., Volume 41, Number 2 (2013), 670-692.

Dates
First available in Project Euclid: 26 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1366980561

Digital Object Identifier
doi:10.1214/13-AOS1094

Mathematical Reviews number (MathSciNet)
MR3023983

Zentralblatt MATH identifier
1267.62084

Subjects
Primary: 62L10: Sequential analysis

Keywords
Change-point detection multi-sensor

Citation

Xie, Yao; Siegmund, David. Sequential multi-sensor change-point detection. Ann. Statist. 41 (2013), no. 2, 670--692. doi:10.1214/13-AOS1094. https://projecteuclid.org/euclid.aos/1366980561


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