Source: Ann. Appl. Stat. Volume 5, Number 2A
(2011), 1102-1125.
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.
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