7 research outputs found
On Asymptotic Optimality of the Second Order in the Minimax Quickest Detection Problem of Drift Change for Brownian Motion
Numerical Comparison of Cusum and Shiryaev-Roberts Procedures for Detecting Changes in Distributions
The CUSUM procedure is known to be optimal for detecting a change in
distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure
is optimal for detecting a change that occurs at a distant time horizon. As a
simpler alternative to the conventional Monte Carlo approach, we propose a
numerical method for the systematic comparison of the two detection schemes in
both settings, i.e., minimax and for detecting changes that occur in the
distant future. Our goal is accomplished by deriving a set of exact integral
equations for the performance metrics, which are then solved numerically. We
present detailed numerical results for the problem of detecting a change in the
mean of a Gaussian sequence, which show that the difference between the two
procedures is significant only when detecting small changes.Comment: 21 pages, 8 figures, to appear in Communications in Statistics -
Theory and Method