  The modified Cholesky decomposition is commonly used for precision matrix
estimation given a specified order of random variables. However, the order of
variables is often not available or cannot be pre-determined. In this work, we
propose to address the variable order issue in the modified Cholesky
decomposition for sparse precision matrix estimation. The key idea is to
effectively combine a set of estimates obtained from multiple permutations of
variable orders, and to efficiently encourage the sparse structure for the
resultant estimate by the thresholding technique on the ensemble Cholesky
factor matrix. The consistent property of the proposed estimate is established
under some weak regularity conditions. Simulation studies are conducted to
evaluate the performance of the proposed method in comparison with several
existing approaches. The proposed method is also applied into linear
discriminant analysis of real data for classification.
