论文标题
基于回顾性CUSUM统计数据的开放端非参数顺序更改点检测
Open-end nonparametric sequential change-point detection based on the retrospective CUSUM statistic
论文作者
论文摘要
在线监视的目的是在收集的观察结果中有大量证据表明基础数据生成机制发生了变化，就会发出警报。这项工作与可以解释为统计检验的开放式非参数程序有关。所提出的监视方案包括计算每个新观察结果到达后所谓的回顾性cusum统计量（或其较小的变化）。在为所选检测器提出合适的阈值函数之后，在监测平均性和相关替代方案的无效假设下的平均值变化的特殊情况下，研究了该程序的渐近有效性。为了在实践中进行顺序测试，使用基于渐近回归模型的方法来估计相关限制分布的大量分位数。蒙特卡洛实验证明了所提出的监测方案的良好有限样本行为，并建议它们优于现有竞争对手，只要在监测开始时不会发生变化。简要讨论了表现出表现出渐近平均行为的统计数据的扩展。最后，在温度异常数据上简要说明了派生的顺序更改点检测测试的应用。
The aim of online monitoring is to issue an alarm as soon as there is significant evidence in the collected observations to suggest that the underlying data generating mechanism has changed. This work is concerned with open-end, nonparametric procedures that can be interpreted as statistical tests. The proposed monitoring schemes consist of computing the so-called retrospective CUSUM statistic (or minor variations thereof) after the arrival of each new observation. After proposing suitable threshold functions for the chosen detectors, the asymptotic validity of the procedures is investigated in the special case of monitoring for changes in the mean, both under the null hypothesis of stationarity and relevant alternatives. To carry out the sequential tests in practice, an approach based on an asymptotic regression model is used to estimate high quantiles of relevant limiting distributions. Monte Carlo experiments demonstrate the good finite-sample behavior of the proposed monitoring schemes and suggest that they are superior to existing competitors as long as changes do not occur at the very beginning of the monitoring. Extensions to statistics exhibiting an asymptotic mean-like behavior are briefly discussed. Finally, the application of the derived sequential change-point detection tests is succinctly illustrated on temperature anomaly data.
