期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 157, 期 -, 页码 45-52出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2017.03.001
关键词
Covariance matrix calibration; Nearness problem; Non-positive definiteness; Spectral decomposition
资金
- MRC [G0902108] Funding Source: UKRI
- Medical Research Council [G0902108, G1000744] Funding Source: researchfish
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. (C) 2017 Elsevier Inc. All rights reserved.
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