论文标题
窗口限制的库司进行顺序更改检测
Window-Limited CUSUM for Sequential Change Detection
论文作者
论文摘要
我们研究了参数在线更改点检测问题，其中流数据的基本分布从已知分布变为已知参数形式但未知参数的替代方案。我们提出了一种联合检测/估计方案，我们称之为窗口限制的cusum，该方案将累积总和（cusum）测试与基于滑动窗口的基于窗口的一致估计值结合在一起。我们表征了窗口尺寸的最佳选择，并表明窗口限制的库us具有渐近级最优性，因为在窗口长度的最佳选择下，平均运行长度接近无穷大。与具有相似渐近优化属性的现有方案相比，我们的测试可以更快地计算出来，因为它可以通过使用后变化后参数的估计来递归地更新Cusum统计量。还提出了一个并行的变体，以促进测试的实际实施。数值模拟证实了我们的理论发现。
We study the parametric online changepoint detection problem, where the underlying distribution of the streaming data changes from a known distribution to an alternative that is of a known parametric form but with unknown parameters. We propose a joint detection/estimation scheme, which we call Window-Limited CUSUM, that combines the cumulative sum (CUSUM) test with a sliding window-based consistent estimate of the post-change parameters. We characterize the optimal choice of the window size and show that the Window-Limited CUSUM enjoys first-order asymptotic optimality as average run length approaches infinity under the optimal choice of window length. Compared to existing schemes with similar asymptotic optimality properties, our test can be much faster computed because it can recursively update the CUSUM statistic by employing the estimate of the post-change parameters. A parallel variant is also proposed that facilitates the practical implementation of the test. Numerical simulations corroborate our theoretical findings.
