On the Minimax Optimality of the CUSUM Statistic in Disorder Problems for Brownian Motion

DOI10.1137/S0040585X97T988447zbMath1380.62234OpenAlexW2780250765MaRDI QIDQ4602305

Albert N. Shiryaev

Publication date: 9 January 2018

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97t988447

zbMATH Keywords

Brownian motiondisorderItô formulaCUSUM statisticprobabilistic characteristicsminimax criteriontwo-sided inequalities for minimax risk

Mathematics Subject Classification ID

Minimax procedures in statistical decision theory (62C20) Brownian motion (60J65) Sequential statistical analysis (62L10)

Related Items (2)

Asymptotic properties of \(M\)-estimators based on estimating equations and censored data in semi-parametric models with multiple change points ⋮ Asymptotic properties of semiparametric \(M\)-estimators with multiple change points

Cites Work

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• Quickest Detection
• Minimax optimality of the method of cumulative sums (cusum) in the case of continuous time
• Procedures for Reacting to a Change in Distribution
• CONTINUOUS INSPECTION SCHEMES

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