A Cholesky-based estimation for large-dimensional covariance matrices

ABSTRACT

This paper develops a new method to estimate a large-dimensional covariance matrix when the variables have no natural ordering among themselves. The modified Cholesky decomposition technique is used to provide a set of estimates of the covariance matrix under multiple orderings of variables. The proposed estimator is in the form of a linear combination of these available estimates and the identity matrix. It is positive definite and applicable in large dimensions. The merits of the proposed estimator are demonstrated through the numerical study and a real data example by comparison with several existing methods.

KEYWORDS:

• Cholesky factor
• ensemble estimate
• large-dimensional
• ordering of variables
• positive definite

Acknowledgements

The authors thank the Associate Editor and two referees for their insightful and helpful comments that have significantly improved the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Xiaoning Kang http://orcid.org/0000-0003-0394-6240

Additional information

Funding

Xiaoning Kang's research was supported by the Science Education Foundation of Liaoning Province (LN2019Q21), and the National Natural Science Foundation of China (71871047). Chaoping Xie's research was supported by the National Natural Science Foundation of China (71903090). Mingqiu Wang's research was supported by the National Natural Science Foundation of China (11771250), and the Natural Science Foundation of Shandong Province (ZR2019MA002).