Longitudinal Graphical Models

• Activity Number: 287
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Quanquan Gu and Yuan Cao and Yang Ning and Han Liu*
• Companies: Princeton University and Princeton University and Princeton University and Princeton University
• Keywords: high dimensional inference ; longitudinal data ; graph estimation ; uncertainty assessment ; post-regularization inference

Abstract

We propose a new family of semiparametric graphical models for analyzing multivariate longitudinal data. In particular, we model the joint distribution of the variables across different subjects by assuming that the distribution of each subject is Gaussian with a subject-specific mean parameter and a common precision matrix which encodes the graph. For graph estimation, we propose a novel parameter estimation method based on the QR transformation of the data. We show that such a procedure is invariant to the subject-specific component and attains the optimal parametric rates of convergence for precision matrix estimation under different norms. We also develop a unified inferential framework for uncertainty assessment.