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

Yajun Mei
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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 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.

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Yajun Mei. 2006-05-15. Sequential change-point detection when unknown parameters are present in the pre-change distribution. https://doi.org/10.1214/009053605000000859

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