Functional connectivity: Shrinkage estimation and randomization test

Mark Fiecas, Hernando Ombao*, Crystal Linkletter, Wesley Thompson, Jerome Sanes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3005-3014
Number of pages10
Issue number4
StatePublished - Feb 15 2010
Externally publishedYes


  • Multivariate time series
  • Partial coherence
  • Randomization test
  • Shrinkage estimator

ASJC Scopus subject areas

  • Neurology
  • Cognitive Neuroscience


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