The Annals of Statistics

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

Yajun Mei

Full-text: Open access

Abstract

In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution fθ and tries to minimize the detection delay for every possible post-change distribution gλ. 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 fθ. 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 fθ and the post-change distribution gλ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.

Article information

Source
Ann. Statist., Volume 34, Number 1 (2006), 92-122.

Dates
First available in Project Euclid: 2 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1146576257

Digital Object Identifier
doi:10.1214/009053605000000859

Mathematical Reviews number (MathSciNet)
MR2275236

Zentralblatt MATH identifier
1091.62064

Subjects
Primary: 62L10: Sequential analysis 62L15: Optimal stopping [See also 60G40, 91A60]
Secondary: 62F05: Asymptotic properties of tests

Keywords
Asymptotic optimality change-point optimizer power one tests quality control statistical process control surveillance

Citation

Mei, Yajun. Sequential change-point detection when unknown parameters are present in the pre-change distribution. Ann. Statist. 34 (2006), no. 1, 92--122. doi:10.1214/009053605000000859. https://projecteuclid.org/euclid.aos/1146576257


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