Teoriya Veroyatnostei i ee Primeneniya
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 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)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2017, 61:4, 719–726

Bibliographic databases:

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
\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 \mathnet{http://mi.mathnet.ru/tvp5090} \crossref{https://doi.org/10.4213/tvp5090} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3632537} \zmath{https://zbmath.org/?q=an:1380.62234} \elib{https://elibrary.ru/item.asp?id=28119215} \transl \jour Theory Probab. Appl. \yr 2017 \vol 61 \issue 4 \pages 719--726 \crossref{https://doi.org/10.1137/S0040585X97T988447} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000418655700011} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85039146902}