title: Functional connectivity: shrinkage estimation and randomization test.
abstract: We develop new statistical methods for estimating functional connectivity between components of a multivariate time series and for testing differences in functional connectivity across experimental conditions. Here, we characterize functional connectivity by partial coherence, which identifies the frequency band (or bands) that drives the direct linear association between any pair of components of a multivariate time series after removing the linear effects of the other components. Partial coherence can be efficiently estimated using the inverse of the spectral density matrix. However, when the number of components is large and the components of the multivariate time series are highly correlated, the spectral density matrix estimate may be numerically unstable and consequently gives partial coherence estimates that are highly variable. To address the problem of numerical instability, we propose a shrinkage-based estimator which is a weighted average of a smoothed periodogram estimator and a scaled identity matrix with frequency-specific weight computed objectively so that the resulting shrinkage estimator minimizes the mean-squared error criterion. Compared to typical smoothing-based estimators, the shrinkage estimator is more computationally stable and gives a lower mean squared error. In addition, we develop a randomization method for testing differences in functional connectivity networks between experimental conditions. Finally, we report results from numerical experiments and analyze an EEG data set recorded during a visually-guided hand movement task.
authors.affiliation: Center for Statistical Sciences, Brown University, Providence, RI, USA.
authors.forename: Mark
authors.initials: M
authors.lastname: Fiecas
authors.forename: Hernando
authors.initials: H
authors.lastname: Ombao
authors.forename: Crystal
authors.initials: C
authors.lastname: Linkletter
authors.forename: Wesley
authors.initials: W
authors.lastname: Thompson
authors.forename: Jerome
authors.initials: J
authors.lastname: Sanes
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004569:Electroencephalography / Q000379:methods*; D005071:Evoked Potentials / Q000502:physiology*; D005260:Female; D006801:Humans; D008297:Male; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D055815:Young Adult