1,391 research outputs found
Partial Coherence Estimation via Spectral Matrix Shrinkage under Quadratic Loss
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 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 robust
and reliable. 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
Random Matrix Derived Shrinkage of Spectral Precision Matrices
Much research has been carried out on shrinkage methods for real-valued
covariance matrices. In spectral analysis of -vector-valued time series
there is often a need for good shrinkage methods too, most notably when the
complex-valued spectral matrix is singular. The equivalent of the Ledoit-Wolf
(LW) covariance matrix estimator for spectral matrices can be improved on using
a Rao-Blackwell estimator, and using random matrix theory we derive its form.
Such estimators can be used to better estimate inverse spectral (precision)
matrices too, and a random matrix method has previously been proposed and
implemented via extensive simulations. We describe the method, but carry out
computations entirely analytically, and suggest a way of selecting an important
parameter using a predictive risk approach. We show that both the Rao-Blackwell
estimator and the random matrix estimator of the precision matrix can
substantially outperform the inverse of the LW estimator in a time series
setting. Our new methodology is applied to EEG-derived time series data where
it is seen to work well and deliver substantial improvements for precision
matrix estimation
Measurement of the 18Ne(a,p_0)21Na reaction cross section in the burning energy region for X-ray bursts
The 18Ne(a,p)21Na reaction provides one of the main HCNO-breakout routes into
the rp-process in X-ray bursts. The 18Ne(a,p_0)21Na reaction cross section has
been determined for the first time in the Gamow energy region for peak
temperatures T=2GK by measuring its time-reversal reaction 21Na(p,a)18Ne in
inverse kinematics. The astrophysical rate for ground-state to ground-state
transitions was found to be a factor of 2 lower than Hauser-Feshbach
theoretical predictions. Our reduced rate will affect the physical conditions
under which breakout from the HCNO cycles occurs via the 18Ne(a,p)21Na
reaction.Comment: 5 pages, 3 figures, accepted for publication on Physical Review
Letter
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