Geodesic
On mini-max optimality of CUSUM statistics in change point detection problem for Brownian motion
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 837-844

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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
Mots-clés : Itô formula. 
@article{TVP_2016_61_4_a10,
     author = {A. N. Shiryaev},
     title = {On mini-max optimality of {CUSUM} statistics in change point detection problem for {Brownian} motion},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {837--844},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a10/}
}
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A. N. Shiryaev. On mini-max optimality of CUSUM statistics in change point detection problem for Brownian motion. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 837-844. http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a10/