Abstract: In this paper, we propose a class of monitoring statistics for a mean shift in a sequence of high-dimensional observations. Inspired by recent U-statistic based retrospective tests, we extend the U-statistic-based approach to the sequential monitoring problem by developing a new adaptive monitoring procedure that can detect both dense and sparse changes in real time. Unlike existing methods in retrospective testing that use self-normalization, we introduce a class of estimators for the q-norm of the covariance matrix and prove their ratio consistency. To facilitate fast computation, we further develop recursive algorithms to improve the computational efficiency of the monitoring procedure. The advantages of the proposed methodology are demonstrated using simulation studies and real-data illustrations.

Key words and phrases: Change point detection, sequential monitoring, sequential testing, U-statistics.