Ridge estimation of inverse covariance matrices from high-dimensional data

The ridge estimation of the precision matrix is investigated in the setting where the number of variables is large relative to the sample size. First, two archetypal ridge estimators are reviewed and it is noted that their penalties do not coincide with common quadratic ridge penalties. Subsequently, starting from a proper ℓ2ℓ2-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.