Truncated Sequential Change-point Detection based on Renewal Counting Processes
Truncated Sequential Change-point Detection based on Renewal Counting Processes
复制标题
基于更新计数过程的截断顺序变化点检测
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Steinebach
中科院分区：
文献类型：
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作者：
A. Gut;J. Steinebach
变点理论的典型方法是基于固定大小的样本进行统计分析。或者，人们依次观察一些随机现象，一旦观察到与“正常”行为有统计学意义的偏差，就采取行动。基于，也许，更现实的情况下，该过程只能被部分观察到，我们认为计数过程中观察到的原始过程在等距的时间点，之后采取行动或不取决于这些时间点之间的观察数量。为了使程序在一切就绪时也能停止，我们引入了一个固定的时间范围n，如果观察到的数据在此之前没有提出任何行动，我们就停止宣布“没有变化”。我们提出了一些停止规则，并考虑他们的渐近下的零假设，以及根据替代品。证明的主要依据是更新过程的强不变性原理和高斯过程的极值渐进性。
The typical approach in change-point theory is to perform the statistical analysis based on a sample of fixed size. Alternatively, one observes some random phenomenon sequentially and takes action as soon as one observes some statistically significant deviation from the “normal” behaviour. Based on the, perhaps, more realistic situation that the process can only be partially observed, we consider the counting process related to the original process observed at equidistant time points, after which action is taken or not depending on the number of observations between those time points. In order for the procedure to stop also when everything is in order, we introduce a fixed time horizon n at which we stop declaring “no change” if the observed data did not suggest any action until then. We propose some stopping rules and consider their asymptotics under the null hypothesis as well as under alternatives. The main basis for the proofs are strong invariance principles for renewal processes and extreme value asymptotics for Gaussian processes.