A calibration method for non-positive definite covariance matrix in multivariate data analysis

Huang, Chao; Farewell, Daniel; Pan, Jianxin

Abstract

Covariance matrices that fail to be positive definite arise often in covariance estimation. Approaches addressing this problem exist, but are not well supported theoretically. In this paper, we propose a unified statistical and numerical matrix calibration, finding the optimal positive definite surrogate in the sense of Frobenius norm. The proposed algorithm can be directly applied to any estimated covariance matrix. Numerical results show that the calibrated matrix is typically closer to the true covariance, while making only limited changes to the original covariance structure.

Citation

Huang, C., Farewell, D., & Pan, J. (2017). A calibration method for non-positive definite covariance matrix in multivariate data analysis. Journal of Multivariate Analysis, 157, 45-52. https://doi.org/10.1016/j.jmva.2017.03.001

• Journal Article Type: Article
• Acceptance Date: Mar 1, 2017
• Online Publication Date: Mar 10, 2017
• Publication Date: 2017-05
• Deposit Date: Jul 30, 2019
• Publicly Available Date: Jul 30, 2019
• Journal: Journal of Multivariate Analysis
• Print ISSN: 0047-259X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 157
• Pages: 45-52
• DOI: https://doi.org/10.1016/j.jmva.2017.03.001
• Keywords: Covariance matrix calibration; Nearness problem; Non-positive definiteness; Spectral decomposition
• Public URL: https://hull-repository.worktribe.com/output/2019932
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0047259X17301343?via%3Dihub#!
• Additional Information: This is the accepted manuscript of an article published in Journal of multivariate analysis, 2017. The version of record is available at the DOI link in this record.; ©2019, Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
• Contract Date: Jul 30, 2019