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

作者：Huang Chao; Farewell Daniel; Pan Jianxin^*

来源：Journal of Multivariate Analysis, 2017, 157: 45-52.

DOI：10.1016/j.jmva.2017.03.001

• Covariance matrix calibration
• Nearness problem
• Non-positive definiteness
• Spectral decomposition

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.

• 出版日期2017-5