FRG Biweekly Meeting: Ping-Shou Zhong, UIC

Title: Statistical Inference for High-dimensional Covariance and Graphical Models

Speaker: Ping-Shou Zhong, UIC

Abstract: In this talk, I will present two statistical inference problems for high dimensional covariance and graphical models. In the first part of the talk, I will introduce change point problems for high-dimensional covariance matrices. We consider high-dimensional functional data with a dense number of repeated measurements taken for a large number of variables from a small number of experimental units. An application to fMRI data demonstrates that our proposed methods can identify event boundaries in the preface of the movie Sherlock. In the second part of the talk, I will introduce a goodness-of-fits test for high-dimensional Gaussian graphical models. We develop a novel consistency-empowered test statistic when the true structure is nested in the postulated structure, by amplifying the noise incurred in estimation. As an application, we apply the test to the analysis of a COVID-19 data set, demonstrating that our test can serve as a tool in choosing an appropriate graph structure to improve estimation efficiency.