A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the precision matrix based on the connection between the known graphical structure and the precision matrix. We obtain the rates of convergence of the proposed estimators and derive the asymptotic normality of the proposed estimator in the high-dimensional setting when the data dimension grows with the sample size. Numerical simulations are conducted to demonstrate the performance of the proposed method. We also show that the proposed method outperforms some existing methods that do not utilize the graphical structure information.

翻译：精确矩阵是一个共变矩阵的反面。 在本文中, 我们研究在高维设置下用已知图形结构来估计精确矩阵的问题。 我们根据已知图形结构与精确矩阵之间的联系, 提议一个简单的精确矩阵估计符。 我们获取了拟议估算器的趋同率, 并得出了在高维环境中, 当数据尺寸随着样本大小的增长而增长时, 提议的估算器的无症状常性。 进行了数值模拟以显示拟议方法的性能。 我们还表明, 拟议的方法优于不使用图形结构信息的某些现有方法。