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February 2006 Sequential change-point detection when unknown parameters are present in the pre-change distribution
Yajun Mei
Ann. Statist. 34(1): 92-122 (February 2006). DOI: 10.1214/009053605000000859


In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution fθ and tries to minimize the detection delay for every possible post-change distribution gλ. In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for every possible pre-change distribution fθ. We present asymptotically optimal procedures for one-parameter exponential families. Next, we develop a general theory for change-point problems when both the pre-change distribution fθ and the post-change distribution gλ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.


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Yajun Mei. "Sequential change-point detection when unknown parameters are present in the pre-change distribution." Ann. Statist. 34 (1) 92 - 122, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62064
MathSciNet: MR2275236
Digital Object Identifier: 10.1214/009053605000000859

Primary: 62L10 , 62L15
Secondary: 62F05

Keywords: asymptotic optimality , Change-point , optimizer , Power one tests , quality control , statistical process control , surveillance

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2006
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