A0444
Title: Adaptive matrix change point detection: Leveraging structured mean shifts
Authors: Xinyu Zhang - Univerisity of Iowa (United States) [presenting]
Kung-Sik Chan - University of Iowa (United States)
Abstract: In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. The focus is on detecting mean shifts with unknown change point locations in these matrix time series. Series that are activated by a change may cluster along certain rows (columns), which forms mode-specific change point alignment. Leveraging mode-specific change point alignments may substantially enhance the power for change point detection. Yet, there may be no mode-specific alignments in the change point structure. A powerful test is proposed to detect mode-specific change points, yet robust to non-mode-specific changes. It shows the validity of using the multiplier bootstrap to compute the p-value of the proposed methods and derive non-asymptotic bounds based on the size and power of the tests. A parallel bootstrap is also proposed as a computationally efficient approach for computing the p-value of the proposed adaptive test. In particular, the consistency of the proposed test is shown under mild regularity conditions. To obtain the theoretical results, new, sharp bounds on Gaussian approximation and multiplier bootstrap approximation are derived, which are of independent interest for high dimensional problems with diverging sparsity.
