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.
Publié le : 2006-02-14
Classification:
Asymptotic optimality,
change-point,
optimizer,
power one tests,
quality control,
statistical process control,
surveillance,
62L10,
62L15,
62F05
@article{1146576257,
author = {Mei, Yajun},
title = {Sequential change-point detection when unknown parameters are present in the pre-change distribution},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 92-122},
language = {en},
url = {http://dml.mathdoc.fr/item/1146576257}
}
Mei, Yajun. Sequential change-point detection when unknown parameters are present in the pre-change distribution. Ann. Statist., Tome 34 (2006) no. 1, pp. 92-122. http://gdmltest.u-ga.fr/item/1146576257/