Presenter: Dr. Ping-Shou Zhong, University of Illinois Chicago

Time: 11:00 AM Central Time, Monday, April 25, 2022

Title: Change-point detection and identification for high-dimensional functional data

Abstract: We consider inference problems for high-dimensional functional data with $p$ functional curves from $n$ experiment units for either sparse or dense repeated measurements ($T$). The number of curves ($p$) could be greater than both $n$ and $T$. The spatial and temporal dependence and high dimensionality pose theoretical and computational challenges. Computationally efficient and tuning-free procedures are developed to detect and identify change points among covariance matrices. The weak convergence of the proposed statistics is established under the “large $p$, small $n$” settings. We further show that the locations of the change points (if exist) can be estimated consistently. The estimator's rate of convergence is shown to depend on the data dimension, sample size, number of repeated measurements, and signal-to-noise ratio. Our proposed algorithms can significantly reduce the computation time. Simulation results demonstrate both the finite sample performance and the computational effectiveness of our proposed procedures. Applications to genomics and fMRI data sets will also be presented.

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