Shrinkage estimation of spectral matrices: A EEG analysis centered approach

In the analysis of Electroencephalograms (EEG), notably in their graphical modeling, the estimation of the spectral matrix and associated variables is of central importance. Often, when adjusting for the bandwidth of the spectral matrix estimate, singularity issues arise and information derived from the inverse spectral matrix is intractable. This requires the use of regularization methods, which have proven very popular in recent research. However, regularisation can be suboptimal for understanding connections within multichannel data and building graphical models. We propose a protocol that addresses this issue and that is specifically designed for spectral matrices of EEG data. It aims at maximising information retention for edge estimation in a graph, and unlike any existing regularisation method it solely relies on available data even at a conceptual level.