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An Optimal Retrospective Change Point Detection Policy

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  • ALBERT VEXLER
  • CHENGQING WU

Abstract

. Since the middle of the twentieth century, the problem of making inferences about the point in a surveyed series of observations at which the underlying distribution changes has been extensively addressed in the economics, biostatistics and statistics literature. Cumulative sum‐type statistics have commonly been thought to play a central role in non‐sequential change point detections. Alternatively, we present and examine an approach based on the Shiryayev–Roberts scheme. We show that retrospective change point detection policies based on Shiryayev–Roberts statistics are non‐asymptotically optimal in the context of most powerful testing.

Suggested Citation

  • Albert Vexler & Chengqing Wu, 2009. "An Optimal Retrospective Change Point Detection Policy," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 542-558, September.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:542-558
    DOI: 10.1111/j.1467-9469.2008.00636.x
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    References listed on IDEAS

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    1. Gombay, Edit & Horváth, Lajos, 1994. "An application of the maximum likelihood test to the change-point problem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 161-171, March.
    2. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    3. Ashish Sen & S. Srivastava, 1975. "On tests for detecting change in mean when variance is unknown," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 479-486, December.
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