## 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 language | English (US) |
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Pages (from-to) | 92-122 |

Number of pages | 31 |

Journal | Annals of Statistics |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - 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