A Binning Approach to Quickest Change Detection With Unknown Postchange Distribution
A Binning Approach to Quickest Change Detection With Unknown Postchange Distribution
复制标题
一种利用未知变化后分布实现最快变化检测的分箱方法
DOI：
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复制
发表时间：
2018
影响因子：
5.4
通讯作者：
V. Veeravalli
中科院分区：
文献类型：
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作者：
T. S. Lau;Wee Peng Tay;V. Veeravalli
最快检测分布变化的问题被认为是在假设的前提下，变化前的分布是已知的，和变化后的分布是唯一已知的属于一个家庭的分布区别于离散化版本的变化前的分布。提出了一种顺序变化检测过程，该过程将样本空间划分为有限数量的箱，并监视落入这些箱中的每个箱中的样本的数量以检测变化。开发了一种近似广义似然比检验的检验统计量。结果表明，建议的检验统计量可以有效地计算使用递归更新计划，并提供了一个程序，用于选择在该计划中的箱数。各种渐近性质的测试统计量推导出的平均检测延迟和平均游程长度虚警之间的性能权衡提供见解。合成和真实的数据的测试表明，我们的方法是相当或更好的性能，现有的非参数变化检测方法。
The problem of quickest detection of a change in distribution is considered under the assumption that the prechange distribution is known, and the postchange distribution is only known to belong to a family of distributions distinguishable from a discretized version of the prechange distribution. A sequential change detection procedure is proposed that partitions the sample space into a finite number of bins and monitors the number of samples falling into each of these bins to detect the change. A test statistic that approximates the generalized likelihood ratio test is developed. It is shown that the proposed test statistic can be efficiently computed using a recursive update scheme, and a procedure for choosing the number of bins in the scheme is provided. Various asymptotic properties of the test statistic are derived to offer insights into its performance tradeoff between average detection delay and average run length to false alarm. Testing on synthetic and real data demonstrates that our approach is comparable or better in the performance to existing nonparametric change detection methods.