Title: An Improved Modified Cholesky Decomposition Method for Inverse Covariance Matrix Estimation,
Abstract: The modified Cholesky decomposition is commonly used for inverse covariance
matrix estimation given a specified order of random variables. However, the
order of variables is often not available or cannot be pre-determined. Hence,
we propose a novel estimator to address the variable order issue in the
modified Cholesky decomposition to estimate the sparse inverse covariance
matrix. 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 use of thresholding
technique on the combined Cholesky factor matrix. The consistent property of
the proposed estimate is established under some weak regularity conditions.
Simulation studies show the superior performance of the proposed method in
comparison with several existing approaches. We also apply the proposed method
into the linear discriminant analysis for analyzing real-data examples for
classification.