Max-Type and Sum-Type Procedures for Online Change-Point Detection in the Mean of High-Dimensional Data

Abstract

We propose two procedures to detect a change in the mean of high-dimensional online data. One is based on a max-type U-statistic and another is based on a sum-type U-statistic. Theoretical properties of the two procedures are explored in the high dimensional setting. More precisely, we derive their average run lengths (ARLs) when there is no change point, and expected detection delays (EDDs) when there is a change point. Accuracy of the theoretical results is confirmed by simulation studies. The practical use of the proposed procedures is demonstrated by detecting an abrupt change in PM2.5 concentrations. The current study attempts to extend the results of the CUSUM and Shiryayev-Roberts procedures previously established in the univariate setting.