The generalized shrinkage estimator for the analysis of functional connectivity of brain signals

Mark Fiecas*, Hernando Ombao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


We develop a new statistical method for estimating functional connectivity between neurophysiological signals represented by a multivariate time series. We use partial coherence as the measure of functional connectivity. Partial coherence identifies the frequency bands that drive the direct linear association between any pair of channels. To estimate partial coherence, one would first need an estimate of the spectral density matrix of the multivariate time series. Parametric estimators of the spectral density matrix provide good frequency resolution but could be sensitive when the parametric model is misspecified. Smoothing-based nonparametric estimators are robust to model misspecification and are consistent but may have poor frequency resolution. In this work, we develop the generalized shrinkage estimator, which is a weighted average of a parametric estimator and a nonparametric estimator. The optimal weights are frequency-specific and derived under the quadratic risk criterion so that the estimator, either the parametric estimator or the nonparametric estimator, that performs better at a particular frequency receives heavier weight. We validate the proposed estimator in a simulation study and apply it on electroencephalogram recordings from a visual-motor experiment.

Original languageEnglish (US)
Pages (from-to)1102-1125
Number of pages24
JournalAnnals of Applied Statistics
Issue number2 A
StatePublished - Jun 2011
Externally publishedYes


  • Multivariate time series
  • Periodogram matrix
  • Shrinkage
  • Spectral density matrix
  • Vector autoregressive model

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'The generalized shrinkage estimator for the analysis of functional connectivity of brain signals'. Together they form a unique fingerprint.

Cite this