Title: Covariance change point detection and identification with high-dimensional functional data
Authors: Ping-Shou Zhong - University of Illinois at Chicago (United States) [presenting]
Shawn Santo - Duke University (United States)
Abstract: High-dimensional functional data appear in practice when a dense number of repeated measurements is taken on a large number of variables for a relatively small number of experimental units. The spatial temporal dependence and high-dimensional nature of the data structure make statistical analysis a challenge. A procedure is developed to detect and identify change points among covariance matrices from high-dimensional functional data. A new test statistics is proposed for change point detection whose asymptotic distribution is established under mild assumptions. We further estimate the locations of the change points if exist. The estimator is proven to be consistent under a set of mild conditions. Its rate of convergence depends on the data dimension, sample size, number of repeated measurements, and signal-to-noise ratio. Computation efficiency is carefully addressed to cope with the large number of repeated measurements and variables measured. Simulation results demonstrate that the size of the test is well controlled at the nominal level, and the locations of multiple change points can accurately be identified. A functional neuroimaging data set is demonstrated to identify points of change in functional connectivity of the human brain.