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

Chao Huang, Daniel Farewell and Jianxin Pan

Journal of Multivariate Analysis, 2017, vol. 157, issue C, 45-52

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.

Keywords: Covariance matrix calibration; Nearness problem; Non-positive definiteness; Spectral decomposition (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.jmva.2017.03.001

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