Minimax Robust Quickest Change Detection
Minimax Robust Quickest Change Detection
复制标题
Minimax 稳健最快变化检测
DOI：
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发表时间：
2009
影响因子：
2.5
通讯作者：
Sean P. Meyn
中科院分区：
文献类型：
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作者：
Jayakrishnan Unnikrishnan;V. Veeravalli;Sean P. Meyn
对于最快的变更检测过程，最优性的流行标准是Lorden准则、Pollak准则和Bayesian准则。在本文中，当变更前和变更后的分布不完全已知，但属于已知的不确定性分布类别时，考虑了这些最快的变更检测问题的鲁棒版本。对于满足特定条件的不确定性类，可以从不确定性类中识别出最不有利分布（LFDs），使得为LFDs设计的检测规则在极小极大意义上对鲁棒问题是最优的。该条件类似于Huber最初研究的稳健假设检验问题中lfd的识别所需的条件。在最优性的Lorden准则下，在渐近设置下，得到了鲁棒性检验所引起的延迟的上界。这个界限量化了为了保证鲁棒性而产生的延迟惩罚。当lfd可以被识别时，建议的测试比基于广义似然比（GLR）统计量的CUSUM测试更容易实现，后者是一种用于此类鲁棒变化检测问题的流行方法。在一些参数值的模拟中，所提出的测试方法也比GLR测试方法具有更好的性能。
The popular criteria of optimality for quickest change detection procedures are the Lorden criterion, the Pollak criterion, and the Bayesian criterion. In this paper, a robust version of these quickest change detection problems is considered when the pre-change and post-change distributions are not known exactly but belong to known uncertainty classes of distributions. For uncertainty classes that satisfy a specific condition, it is shown that one can identify least favorable distributions (LFDs) from the uncertainty classes, such that the detection rule designed for the LFDs is optimal for the robust problem in a minimax sense. The condition is similar to that required for the identification of LFDs for the robust hypothesis testing problem originally studied by Huber. An upper bound on the delay incurred by the robust test is also obtained in the asymptotic setting under the Lorden criterion of optimality. This bound quantifies the delay penalty incurred to guarantee robustness. When the LFDs can be identified, the proposed test is easier to implement than the CUSUM test based on the Generalized Likelihood Ratio (GLR) statistic which is a popular approach for such robust change detection problems. The proposed test is also shown to give better performance than the GLR test in simulations for some parameter values.