Schneider-Luftman, DDSchneider-LuftmanWalden, ATATWalden2016-06-132016-06-202016-06-20IEEE Transactions on Signal Processing, 2016, 64 (22), pp.5767-57771941-0476http://hdl.handle.net/10044/1/33619Partial coherence is an important quantity derived from spectral or precision matrices and is used in seismology, meteorology, oceanography, neuroscience and elsewhere. If the number of complex degrees of freedom only slightly exceeds the dimension of the multivariate stationary time series, spectral matrices are poorly conditioned and shrinkage techniques suggest themselves.When true partial coherencies are quite large then for shrinkage estimators of the diagonal weighting kind it is shown empirically that the minimization of risk using quadratic loss (QL) leads to oracle partial coherence estimators far superior to those derived by minimizing risk using Hilbert-Schmidt (HS) loss. When true partial coherencies are small the methods behave similarly. We derive two new QL estimators for spectral matrices, and new QL and HS estimators for precision matrices. In addition for the full estimation (non-oracle) case where certain trace expressions must also be estimated, we examine the behaviour of three different QL estimators, the precision matrix one seeming particularly appealing. For the empirical study we carry out exact simulations derived from real EEG data for two individuals, one having large, and the other small, partial coherencies. This ensures our study covers cases of real-world relevance.© 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.Science & TechnologyTechnologyEngineering, Electrical & ElectronicEngineeringPartial coherencequadratic lossshrinkageprecision matrixspectral matrixCOVARIANCE MATRICESFUNCTIONAL CONNECTIVITYBRAIN CONNECTIVITYEMPIRICAL BAYESWISHARTMOMENTSNetworking & TelecommunicationsMD MultidisciplinaryJournal Articlehttps://www.dx.doi.org/10.1109/TSP.2016.2582464