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

Huang, Chao, Farewell, Daniel ORCID: https://orcid.org/0000-0002-8871-1653 and Pan, Jianxin 2017. A calibration method for non-positive definite covariance matrix in multivariate data analysis. Journal of Multivariate Analysis 157 , pp. 45-52. 10.1016/j.jmva.2017.03.001

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Medicine
Publisher:	Elsevier
ISSN:	0047-259X
Date of First Compliant Deposit:	29 October 2019
Last Modified:	17 Nov 2024 04:45
URI:	https://orca.cardiff.ac.uk/id/eprint/98928

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