论文标题
基于早期和晚期变化点的U统计量的顺序测试的渐近延迟时间
Asymptotic delay times of sequential tests based on U-statistics for early and late change points
论文作者
论文摘要
顺序更改点测试旨在在控制渐近错误警报错误时发生结构断裂后尽快发出警报。对于此类测试，了解检测到休息的速度尤为重要。尽管通常仅通过模拟来评估这一点，但在本文中，我们根据U统计数据得出了顺序更改点程序的延迟时间的渐近分布。这包括之前已经讨论过的均值（DOM）顺序测试，还包括一个新的可靠Wilcoxon顺序更改点测试。类似于A-tosterii设置中的渐近相对效率，结果使我们能够比较这两个程序的检测延迟。结果表明，Wilcoxon顺序程序对较重的尾部分布的检测延迟较小，这也通过模拟证实。虽然先前的文献仅为早期变化点得出结果，但我们获得了早期和晚变化点的延迟时间的渐近分布。最后，我们评估了通过模拟研究的渐近分布如何近似有限样品的实际停止时间。
Sequential change point tests aim at giving an alarm as soon as possible after a structural break occurs while controlling the asymptotic false alarm error. For such tests it is of particular importance to understand how quickly a break is detected. While this is often assessed by simulations only, in this paper, we derive the asymptotic distribution of the delay time for sequential change point procedures based on U-statistics. This includes the difference-of-means (DOM) sequential test, that has been discussed previously, but also a new robust Wilcoxon sequential change point test. Similar to asymptotic relative efficiency in an a-posteriori setting, the results allow us to compare the detection delay of the two procedures. It is shown that the Wilcoxon sequential procedure has a smaller detection delay for heavier tailed distributions which is also confirmed by simulations. While the previous literature only derives results for early change points, we obtain the asymptotic distribution of the delay time for both early as well as late change points. Finally, we evaluate how well the asymptotic distribution approximates the actual stopping times for finite samples via a simulation study.
