  This article explores the estimation of precision matrices in
high-dimensional Gaussian graphical models. We address the challenge of
improving the accuracy of maximum likelihood-based precision estimation through
penalization. Specifically, we consider an elastic net penalty, which
incorporates both L1 and Frobenius norm penalties while accounting for the
target matrix during estimation. To enhance precision matrix estimation, we
propose a novel two-step estimator that combines the strengths of ridge and
graphical lasso estimators. Through this approach, we aim to improve overall
estimation performance. Our empirical analysis demonstrates the superior
efficiency of our proposed method compared to alternative approaches. We
validate the effectiveness of our proposal through numerical experiments and
application on three real datasets. These examples illustrate the practical
applicability and usefulness of our proposed estimator.
