The modified Cholesky decomposition is popular for inverse covariance
estimation, but often needs pre-specification on the full information of
variable ordering. In this work, we propose a block Cholesky decomposition
(BCD) for estimating inverse covariance matrix under the partial information of
variable ordering, in the sense that the variables can be divided into several
groups with available ordering among groups, but variables within each group
have no orderings. The proposed BCD model provides a unified framework for
several existing methods including the modified Cholesky decomposition and the
Graphical lasso. By utilizing the partial information on variable ordering, the
proposed BCD model guarantees the positive definiteness of the estimated matrix
with statistically meaningful interpretation. Theoretical results are
established under regularity conditions. Simulation and case studies are
conducted to evaluate the proposed BCD model