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.

翻译：本文探讨了高维高斯图形模型中精度矩阵的估计问题。我们致力于通过惩罚方法提升基于最大似然的精度估计的准确性。具体而言，我们考虑弹性网络惩罚，该惩罚同时包含L1范数和Frobenius范数惩罚，并在估计过程中考虑目标矩阵。为优化精度矩阵估计，我们提出一种新颖的两步估计器，融合了脊估计与图形套索估计的优势。通过这一方法，我们旨在提升整体估计性能。实证分析表明，与替代方法相比，我们提出的方法具有优越的效率。通过数值实验及三个真实数据集的应用，我们验证了所提方案的有效性。这些实例展示了我们提出的估计器在实际应用中的适用性和实用性。