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Optimal estimation for a family of sparse covariance matrices with missing data

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  • Liu, Youming
  • Miao, Li

Abstract

Estimation of covariance matrices plays an important role in high-dimensional inference problems. It has been investigated when some observations are missing. The known work usually assume the Gaussian or sub-Gaussian condition of a random vector. Cai and Zhang provide an optimal estimation for a class of sparse covariance matrices H under the sub-Gaussian assumption of a random vector, see T. T. Cai and A. Zhang, Journal of Multivariate Analysis, 2016. This current paper considers the same problem for a larger family of sparse covariance matrices Hɛ(0<ɛ≤2) under some weaker assumptions (not necessarily sub-Gaussian) of a random vector. When ɛ=2, our results generalize a theorem of Cai and Zhang. Numerical experiments are given to support our theoretical analysis.

Suggested Citation

  • Liu, Youming & Miao, Li, 2026. "Optimal estimation for a family of sparse covariance matrices with missing data," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001083
    DOI: 10.1016/j.jmva.2025.105513
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    References listed on IDEAS

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    1. Wang, Xin & Kong, Lingchen & Wang, Liqun, 2024. "Estimation of sparse covariance matrix via non-convex regularization," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    2. Marco Avella-Medina & Heather S Battey & Jianqing Fan & Quefeng Li, 2018. "Robust estimation of high-dimensional covariance and precision matrices," Biometrika, Biometrika Trust, vol. 105(2), pages 271-284.
    3. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    4. Park, Seongoh & Lim, Johan, 2019. "Non-asymptotic rate for high-dimensional covariance estimation with non-independent missing observations," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 113-123.
    5. Cai, T. Tony & Zhang, Anru, 2016. "Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 55-74.
    6. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    7. Cui, Ying & Leng, Chenlei & Sun, Defeng, 2016. "Sparse estimation of high-dimensional correlation matrices," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 390-403.
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