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Published on: November 24, 2021
Directed Transfer Function: Unified Asymptotic Theory and Some of Its Implications
Objective:
To present a unified mathematical derivation of the frequency-dependent asymptotic behavior of the three main forms of directed transfer function (DTF).
Methods:
A synthesis of the results (proved in an extended Appendix) is followed by a series of Monte Carlo simulations of representative examples.
Results:
DTF estimators are asymptotically normal when the true values are different from zero. Under the null hypothesis H0: DTF=0, the estimator is distributed as a linear combination of independent χ21 variables.
Conclusions:
Null DTF rejection is shown to be achievable with identical performance irrespective of which DTF form is adopted.
Significance:
Together with recent allied partial directed coherence results, this paper rounds up connectivity inference tools for a class of frequency-domain connectivity estimators.
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