Shrinkage Estimation and Inferential Procedures for Functional Connectivity

• Activity Number: 101
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Mark Fiecas*+ and Hernando Ombao and Crystal Linkletter and Wesley K. Thompson and Jerome Sanes
• Companies: Brown University and Brown University and Brown University and University of California, San Diego and Brown University
• Keywords: Multivariate time series ; Shrinkage estimator ; Partial coherence ; EEG

Abstract

One current interest in the neuroscience community is modeling connectivity between brain regions and studying how connectivity may change across patient groups and experimental conditions. In this project, we develop methods of estimation and inference for condition-specific functional connectivity, as measured by partial coherence. Partial coherence can be computed efficiently via the inverse of the spectral density matrix. A statistical challenge is that the spectral matrix may be poorly conditioned and thus give numerically unstable estimates of partial coherence. We adopt a shrinkage estimator for the spectral density matrix, which has lower mean-squared error and is more numerically stable than the classical smoothed periodogram estimator. We present simulation results using the shrinkage estimator and analyze an EEG data set.