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Teoriya Veroyatnostei i ee Primeneniya, 2016, Volume 61, Issue 4, Pages 837–844
DOI: https://doi.org/10.4213/tvp5090 (Mi tvp5090) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On mini-max optimality of CUSUM statistics in change point detection problem for Brownian motion

A. N. Shiryaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (180 kB) Citations (2) English version article
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DOI: https://doi.org/10.4213/tvp5090
Abstract: The CUSUM (CUmulative SUM) statistic is a natural generalization of the likelihood ratio. It was observed long ago that this statistic has many remarkable properties, which are useful in empirical analysis of statistical data. In this paper, we consider Lorden's minimax criterion in problems of the quickest detection of disorder, which represents the value of the drift of Brownian motion changes at an unknown and unobservable moment of time. We provide the proof of the optimality for this minimax criterion.
Keywords: disorder, minimax criterion, two-sided inequalities for minimax risk, probabilistic characteristics, Itô formula.
Funding agency Grant number
Russian Science Foundation 15-11-30042
Received: 01.09.2016
English version:
Theory of Probability and its Applications, 2017, Volume 61, Issue 4, Pages 719–726
DOI: https://doi.org/10.1137/S0040585X97T988447
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. N. Shiryaev, “On mini-max optimality of CUSUM statistics in change point detection problem for Brownian motion”, Teor. Veroyatnost. i Primenen., 61:4 (2016), 837–844; Theory Probab. Appl., 61:4 (2017), 719–726
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v61/i4/p837
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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