Statistics – Computation
Scientific paper
2009-08-28
Communications in Statistics - Theory and Methods, vol. 38, no. 16-17, pp. 3225-3239, 2009
Statistics
Computation
21 pages, 8 figures, to appear in Communications in Statistics - Theory and Methods
Scientific paper
10.1080/03610920902947774
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.
Moustakides George V.
Polunchenko Aleksey S.
Tartakovsky Alexander G.
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