The Annals of Statistics
- Ann. Statist.
- Volume 34, Number 1 (2006), 92-122.
Sequential change-point detection when unknown parameters are present in the pre-change distribution
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.
Ann. Statist., Volume 34, Number 1 (2006), 92-122.
First available in Project Euclid: 2 May 2006
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Mei, Yajun. Sequential change-point detection when unknown parameters are present in the pre-change distribution. Ann. Statist. 34 (2006), no. 1, 92--122. doi:10.1214/009053605000000859. https://projecteuclid.org/euclid.aos/1146576257