An improved banded estimation for large covariance matrix

Abstract

The modified Cholesky decomposition (MCD) is a powerful and efficient tool for the large covariance matrix estimation, which guarantees the positive definite property of the estimated matrix. However, when implementing the MCD, it requires a pre-knowledge of the variable ordering, which is often unknown before analysis or does not exist for some real data. In this work, we propose a positive definite Cholesky-based estimate for the large banded covariance matrix by recovering the variable ordering before applying the MCD technique. The asymptotically theoretical convergence rate is established under some regularity conditions. The merits of the proposed model is illustrated by simulation study and applications to two gene expression data sets.

Keywords:

• Banded matrix
• Cholesky factor
• positive definite
• variable ordering

Acknowledgments

The authors thank the reviewers for their constructive comments that have greatly improved the original manuscript.

Additional information

Funding

The authors would like to acknowledge the support from Ministry of Education of China [20YJC910007], National Natural Science Foundation of China [71903090, 71903024], and Science Education Foundation of Liaoning Province [LN2019Q21].