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

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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 prechange 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.

Original languageEnglish (US)
Pages (from-to)92-122
Number of pages31
JournalAnnals of Statistics
Volume34
Issue number1
DOIs
StatePublished - Feb 2006

Keywords

  • Asymptotic optimality
  • Change-point
  • Optimizer
  • Power one tests
  • Quality control
  • Statistical process control
  • Surveillance

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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