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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 4, Pages 837–844 (Mi tvp5090)  

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

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


DOI: https://doi.org/10.4213/tvp5090

Full text: PDF file (180 kB)
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English version:
Theory of Probability and its Applications, 2017, 61:4, 719–726

Bibliographic databases:

Received: 01.09.2016

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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