SEQUENTIAL MULTI-SENSOR CHANGE-POINT DETECTION
成果类型：
Article
署名作者：
Xie, Yao; Siegmund, David
署名单位：
Duke University; Stanford University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/13-AOS1094
发表日期：
2013
页码：
670-692
关键词：
摘要：
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 pp 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.