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Optimal parallel sequential change detection under generalized performance measures

Author

Listed:
  • Lu, Zexian
  • Chen, Yunxiao
  • Li, Xiaoou

Abstract

This paper considers the detection of change points in parallel data streams, a problem widely encountered when analyzing large-scale real-time streaming data. Each stream may have its own change point, at which its data has a distributional change. With sequentially observed data, a decision maker needs to declare whether changes have already occurred to the streams at each time point. Once a stream is declared to have changed, it is deactivated permanently so that its future data will no longer be collected. This is a compound decision problem in the sense that the decision maker may want to optimize certain compound performance metrics that concern all the streams as a whole. Thus, the decisions are not independent for different streams. Our contribution is three-fold. First, we propose a general framework for compound performance metrics that includes the ones considered in the existing works as special cases and introduces new ones that connect closely with the performance metrics for single-stream sequential change detection and large-scale hypothesis testing. Second, data-driven decision procedures are developed under this framework. Finally, optimality results are established for the proposed decision procedures. The proposed methods and theory are evaluated by simulation studies and a case study.

Suggested Citation

  • Lu, Zexian & Chen, Yunxiao & Li, Xiaoou, 2022. "Optimal parallel sequential change detection under generalized performance measures," LSE Research Online Documents on Economics 118348, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:118348
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    File URL: http://eprints.lse.ac.uk/118348/
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    References listed on IDEAS

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    1. Jay Bartroff & Matthew Finkelman & Tze Lai, 2008. "Modern Sequential Analysis and Its Applications to Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 473-486, September.
    2. Savas Dayanik & Christian Goulding & H. Vincent Poor, 2008. "Bayesian Sequential Change Diagnosis," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 475-496, May.
    3. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
    4. Y. Mei, 2010. "Efficient scalable schemes for monitoring a large number of data streams," Biometrika, Biometrika Trust, vol. 97(2), pages 419-433.
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    More about this item

    Keywords

    large-scale inference; multiple change detection; sequential analysis; multiple hypothesis testing;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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