Statistical Models Commons^™

Time series data obtained from neurophysiological signals is often high-dimensional and the length of the time series is often short relative to the number of dimensions. Thus, it is difficult or sometimes impossible to compute statistics that are based on the spectral density matrix because these matrices are numerically unstable. In this work, we discuss the importance of regularization for spectral analysis of high-dimensional time series and propose shrinkage estimation for estimating high-dimensional spectral density matrices. The shrinkage estimator is derived from a penalized log-likelihood, and the optimal penalty parameter has a closed-form solution, which can be estimated using the …

Vector auto-regressive (VAR) models typically form the basis for constructing directed graphical models for investigating connectivity in a brain network with brain regions of interest (ROIs) as nodes. There are limitations in the standard VAR models. The number of parameters in the VAR model increases quadratically with the number of ROIs and linearly with the order of the model and thus due to the large number of parameters, the model could pose serious estimation problems. Moreover, when applied to imaging data, the standard VAR model does not account for variability in the connectivity structure across all subjects. In this paper, …