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Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions

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  • George V. Moustakides
  • Aleksey S. Polunchenko
  • Alexander G. Tartakovsky

Abstract

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.

Suggested Citation

  • George V. Moustakides & Aleksey S. Polunchenko & Alexander G. Tartakovsky, 2009. "Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 38(16-17), pages 3225-3239, October.
    • Handle: RePEc:taf:lstaxx:v:38:y:2009:i:16-17:p:3225-3239
    DOI: 10.1080/03610920902947774
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    Cited by:

    1. Ameur, Hachmi Ben & Han, Xuyuan & Liu, Zhenya & Peillex, Jonathan, 2022. "When did global warming start? A new baseline for carbon budgeting," Economic Modelling, Elsevier, vol. 116(C).
    2. Austin Cooper & Arturo Bretas & Sean Meyn, 2023. "Anomaly Detection in Power System State Estimation: Review and New Directions," Energies, MDPI, vol. 16(18), pages 1-15, September.

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