Skip to main content

Research Repository

Advanced Search

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

Huang, Chao; Farewell, Daniel; Pan, Jianxin

Authors

Daniel Farewell

Jianxin Pan



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 Mar 29, 2024
Journal Journal of Multivariate Analysis
Print ISSN 0047-259X
Electronic ISSN 1095-7243
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/

Files






You might also like



Downloadable Citations