  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.
