  Graphical Gaussian models are popular tools for the estimation of
(undirected) gene association networks from microarray data. A key issue when
the number of variables greatly exceeds the number of samples is the estimation
of the matrix of partial correlations. Since the (Moore-Penrose) inverse of the
sample covariance matrix leads to poor estimates in this scenario, standard
methods are inappropriate and adequate regularization techniques are needed. In
this article, we investigate a general framework for combining regularized
regression methods with the estimation of Graphical Gaussian models. This
framework includes various existing methods as well as two new approaches based
on ridge regression and adaptive lasso, respectively. These methods are
extensively compared both qualitatively and quantitatively within a simulation
study and through an application to six diverse real data sets. In addition,
all proposed algorithms are implemented in the R package "parcor", available
from the R repository CRAN.
