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Minimax Robust Quickest Change Detection

机译：Minimax稳健的最快变化检测

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摘要

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.
机译：最快的变化检测程序的最佳最佳流行准则是Lorden准则，Pollak准则和贝叶斯准则。在本文中，当变化前和变化后的分布不十分确切但属于已知的不确定性分布类别时，可以考虑这些最快的变化检测问题的可靠版本。对于满足特定条件的不确定性类别，表明可以从不确定性类别中识别出最不利的分布（LFD），从而为LFD设计的检测规则在极小极大意义上对于鲁棒问题是最佳的。该条件类似于Huber最初研究的用于鲁棒假设检验问题的LFD识别所需的条件。在最优性的Lorden准则下的渐近设置下，也获得了由鲁棒测试引起的延迟的上限。该界限量化了为保证鲁棒性而产生的延迟损失。当可以识别LFD时，建议的测试比基于广义似然比（GLR）统计量的CUSUM测试更易于实现，这是解决此类鲁棒变化检测问题的常用方法。在某些参数值的仿真中，建议的测试还显示出比GLR测试更好的性能。

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