Partial coherence estimation via spectral matrix shrinkage under quadratic loss
File(s)SLuftmanWaldenQL.pdf (926.43 KB)
Accepted version
Author(s)
Schneider-Luftman, D
Walden, AT
Type
Journal Article
Abstract
Partial 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.
Date Issued
2016-06-20
Date Acceptance
2016-06-10
ISSN
1941-0476
Publisher
IEEE
Start Page
5767
End Page
5777
Journal / Book Title
IEEE Transactions on Signal Processing
Volume
64
Issue
22
Copyright Statement
© 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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Subjects
Science & Technology
Technology
Engineering, Electrical & Electronic
Engineering
Partial coherence
quadratic loss
shrinkage
precision matrix
spectral matrix
COVARIANCE MATRICES
FUNCTIONAL CONNECTIVITY
BRAIN CONNECTIVITY
EMPIRICAL BAYES
WISHART
MOMENTS
Networking & Telecommunications
MD Multidisciplinary
Publication Status
Published