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Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data
We study ridge estimation of the precision matrix in the high-dimensional
setting where the number of variables is large relative to the sample size. We
first review two archetypal ridge estimators and note that their utilized
penalties do not coincide with common ridge penalties. Subsequently, starting
from a common ridge penalty, analytic expressions are derived for two
alternative ridge estimators of the precision matrix. The alternative
estimators are compared to the archetypes with regard to eigenvalue shrinkage
and risk. The alternatives are also compared to the graphical lasso within the
context of graphical modeling. The comparisons may give reason to prefer the
proposed alternative estimators
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