Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the detection delays for the case of extreme sparsity. A sparsity likelihood stopping rule based on sparsity likelihood scores is designed to achieve the optimal detections. A numerical study is also performed to show that the sparsity likelihood stopping rule performs well at all levels of sparsity. We also illustrate its applications on non-normal models.

翻译：考虑多数据流中的序列变点检测问题。我们给出了变点稀疏度各层级下检测延迟的渐近下界，并推导了在极端稀疏情况下更小的渐近下界。设计了一种基于稀疏似然得分的稀疏似然停止规则，以实现最优检测。数值研究显示，该稀疏似然停止规则在所有稀疏度层级均表现良好。我们还展示了其在非正态模型中的应用。