Monitoring High-Dimensional Streaming Data via Fusing Nonparametric Shiryaev-Roberts Statistics

Monitoring high-dimensional streaming data has a wide range of applications in science, engineering, and industry. In this work, we propose an efficient and robust sequential change-point detection algorithm for monitoring high-dimensional streaming data. It has two components. At the local level, we adopt a window-limited nonparametric Shiryaev-Roberts (WL-NPSR) statistic for detecting potential distribution changes at each dimension of the streaming data. At the global level, we fuse local WL-NPSR statistics together to construct a global monitoring statistic via quantile filtering and sum-shrinkage functions. Theoretical analysis and extensive numerical experiments demonstrate the efficiency and robustness of our proposed algorithm.