Spatial rank-based high-dimensional change point detection via random integration

Abstract

Detecting change points is an important task to identify an abrupt and significant change in the data generating process. Traditional change point detection methods are not applicable in high-dimensional situations due to many obstacles, such as the requirement of normality or the estimation of the covariance matrix. This paper presented a novel nonparametric method to overcome such issues by using the random integration with spatial ranks, which is tailored to high-dimensional change point detection problems. The proposed method is a unified framework that includes and extends many existing methods and can effectively handle high-dimensional non-normal data, whose asymptotic properties are established under mild conditions. In addition, we developed a computationally efficient algorithm to calculate the rejection thresholds and an effective post-signal diagnostic procedure to identify the potential directions. Finally, numerical studies together with real data examples demonstrated that the proposed method can identify the change point efficiently.