Sequential change-point detection when unknown parameters are present in the pre-change distribution

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dc.creatorMei, Yajun
dc.date2006-05-12
dc.date2006-05-15
dc.date.accessioned2026-07-07T08:07:48Z
dc.date.available2026-07-07T08:07:48Z
dc.descriptionIn the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution $f_θ$ and tries to minimize the detection delay for every possible post-change distribution $g_λ$. 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 $f_θ$. 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 $f_θ$ and the post-change distribution $g_λ$ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053605000000859 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0605322
dc.identifierhttp://arxiv.org/abs/math/0605322
dc.identifierAnnals of Statistics 2006, Vol. 34, No. 1, 92-122
dc.identifierdoi:10.1214/009053605000000859
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131051
dc.subjectStatistics Theory
dc.subject62L10, 62L15 (Primary) 62F05 (Secondary)
dc.titleSequential change-point detection when unknown parameters are present in the pre-change distribution
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