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.
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
\Bibitem{Shi16}
\by A.~N.~Shiryaev
\paper On mini-max optimality of CUSUM statistics in change point detection problem for Brownian motion
\jour Teor. Veroyatnost. i Primenen.
\yr 2016
\vol 61
\issue 4
\pages 837--844
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\transl
\jour Theory Probab. Appl.
\yr 2017
\vol 61
\issue 4
\pages 719--726
\crossref{https://doi.org/10.1137/S0040585X97T988447}
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Linking options:
https://www.mathnet.ru/eng/tvp5090
https://doi.org/10.4213/tvp5090
https://www.mathnet.ru/eng/tvp/v61/i4/p837
This publication is cited in the following 2 articles:
Salim Bouzebda, Anouar Abdeldjaoued Ferfache, “Asymptotic properties of semiparametric M-estimators with multiple change points”, Physica A: Statistical Mechanics and its Applications, 609 (2023), 128363
S. Bouzebda, A. A. Ferfache, “Asymptotic properties of m-estimators based on estimating equations and censored data in semi-parametric models with multiple change points”, J. Math. Anal. Appl., 497:2 (2021), 124883
Citation in format AMSBIB
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