Nonparametric adaptive change point estimation and on line detection
Nonparametric adaptive change point estimation and on line detection
复制标题
非参数自适应变点估计和在线检测
DOI：
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发表时间：
2000
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通讯作者：
M. Baron
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文献类型：
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作者：
M. Baron
在标准条件下的变点问题的一个或两个分布是未知的，我们提出了有效的在线和离线的非参数算法检测和估计的变点。它们基于直方图密度估计，允许涉及有序和分类数据的应用程序。此外，它们旨在检测分布中的任何变化，而不一定与位置或尺度参数相关。所提出的方案的有效性证明了有关的平均延迟和平均假警报之间的时间不等式。渐近地，他们表现出类似的最有效的程序的基础上已知的分布。停止规则实现了一个渐进的线性平均延迟和指数平均时间之间的虚警。在此基础上，给出了直方图密度估计的阈值选取和区域划分的准则。将所提出的方法应用于英国温度资料和东方冰芯记录，以检测全球气候变化
Under standard conditions of change point problems with one or both distributions being unknown, we propose efficient on line and off line nonparametric algorithms for detecting and estimating the change point. They are based on histogram density estimators, which allows applications involving ordinal and categorical data. Also, they are designed to detect any changes in distribution, not necessarily related to the location or scale parameters. EfFiciency of the proposed schemes is demonstrated by relevant inequalities for the mean delay and the mean time between false alarms. Asymptotically, they are shown to behave similarly to the most efficient procedures based on the known distributions. The stopping rule achieves an asymptotically linear rnean delay and an exponential mean time between false alarms. The guidelines on selecting the threshold and the partition for the histogram density estimation are given, based on the obtained results. Proposed methods are applied to the England temperatures data and the Vostok ice core record to detect the global climate changes