A note on online change point detection

We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common variance factor and piecewise-constant but otherwise unknown means are collected. We develop a simple CUSUM-b...

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Bibliographic Details
Published inSequential analysis Vol. 42; no. 4; pp. 438 - 471
Main Authors Yu, Yi, Madrid Padilla, Oscar Hernan, Wang, Daren, Rinaldo, Alessandro
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.10.2023
Taylor & Francis Ltd
Subjects
cumulative sum statistics
False alarms
Minimax technique
Nonparametric statistics
Normal distribution
Online change point detection
Statistical analysis
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Summary:We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common variance factor and piecewise-constant but otherwise unknown means are collected. We develop a simple CUSUM-based methodology that provably control the probability of false alarms or the average run length while minimizing, in a minimax sense, the detection delay. We allow for all the model parameters to vary in order to capture a broad range of levels of statistical hardness for the problem at hand. We further show how our methodology is applicable to the case in which multiple change points are to be estimated sequentially.
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ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2023.2276170