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

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  • Huang, Chao
  • Farewell, Daniel
  • Pan, Jianxin

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.

Suggested Citation

  • Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.
    • Handle: RePEc:eee:jmvana:v:157:y:2017:i:c:p:45-52
    DOI: 10.1016/j.jmva.2017.03.001
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    Cited by:

    1. Luo, Renwen & Pan, Jianxin, 2022. "Conditional generalized estimating equations of mean-variance-correlation for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    2. Wang, Xuanci & Zhang, Bin, 2024. "Target selection in shrinkage estimation of covariance matrix: A structural similarity approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    3. Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2021. "Estimation and optimal structure selection of high-dimensional Toeplitz covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Peng, Cheng & Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2022. "Latent Gaussian copula models for longitudinal binary data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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