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

• 成果类型: Article
• 署名作者: Mei, YJ
• 署名单位: Fred Hutchinson Cancer Center; California Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000859
• 发表日期: 2006
• 页码: 92-122
• 关键词: average run-length; stopping rules; false alarm; SURVEILLANCE; optimality; regression; systems; tests

摘要

In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution f(theta) and tries to minimize the detection delay for every possible post-change distribution g(lambda). 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(theta). We present asymptotically optimal procedures for one-parameter exponential families. Next, we develop a general theory for change-point problems when both the prechange distribution f(theta) and the post-change distribution g; involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.