Sequential change-point detection when unknown parameters are present in the pre-change distribution
- Creators
- Mei, Yajun
Abstract
In 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.
Additional Information
© 2006 Institute of Mathematical Statistics. Received February 2004; revised February 2005. Supported in part by NIH Grant R01 AI055343. This work is part of my Ph.D. dissertation at the California Institute of Technology. I would like to thank my thesis advisor, Professor Gary Lorden, for his constant support and encouragement and Professor Moshe Pollak for sharing his insightful ideas. Thanks also to Professor Sarah Holte, Professor Jon A. Wellner, the Associate Editor and the referees for their helpful remarks.Attached Files
Published - MEIaos06.pdf
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Additional details
- Eprint ID
- 24551
- Resolver ID
- CaltechAUTHORS:20110726-135615446
- R01 AI055343
- NIH
- Created
-
2011-07-27Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field
- Other Numbering System Name
- Zentralblatt MATH identifier
- Other Numbering System Identifier
- 05034305