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Performance study of change-point detection thresholds for cumulative sum statistic in a sequential context

机译：顺序上下文中累积和统计变化点检测阈值的性能研究

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摘要

Sequential detection is based on a recursive statistic and a threshold it must reach to report a change. In this paper, we consider the score-based cumulative sum statistic and propose to evaluate the detection performance of some thresholds on simulated data. Three thresholds come from the literature: the Wald constant, the empirical constant, and the conditional empirical instantaneous threshold (the latter two are built by a simulation-based procedure). Two new thresholds are built by a simulation-based procedure: the first one is instantaneous, the second is a dynamical version of the previous one. The thresholds' performance measured by an estimation of the mean time between false alarm(MTBFA)and the average detection delay(ADD)are evaluated on independent and autocorrelated data for several scenario, according to the detection objective and the real change in the data. The simulations allow us to compare the difference between the thresholds' results and to see that their performances prove to be robust when a parameter of the prechange regime is misestimated or when the data independence assumption is violated. We found also that the conditional empirical threshold is the best at minimizing the detection delay while maintaining the given false alarm rate. However, on real data, we suggest to use the dynamic instantaneous threshold because it is the easiest to build for practical implementation.
机译：顺序检测基于递归统计信息和它必须达到的阈值以报告更改。在本文中，我们考虑基于分数的累积总和统计，并建议评估模拟数据的一些阈值的检测性能。三个阈值来自文献：沃尔德常数，经验常数和条件经验瞬时阈值（后两者通过基于模拟的过程构建）。通过基于仿真的过程构建了两个新的阈值：第一个是瞬时的，第二个是前一个的动态版本。根据检测目标和数据的真实变化，在独立和自相关数据中估计阈值通过估计误报（MTBFA）与平均检测延迟（ADD）的平均检测延迟（ADD）测量的阈值。仿真允许我们比较阈值的结果之间的差异，并看到它们的性能被证明是稳健的，当预逼制度的参数被误使或违反数据独立假设时。我们发现，条件经验阈值是最大限度地减少检测延迟，同时保持给定的误报率。但是，在实际数据上，我们建议使用动态瞬时阈值，因为它是最容易用于实际实现的。

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