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Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data

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  • Cai, T. Tony
  • Zhang, Anru

Abstract

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:55-74
    DOI: 10.1016/j.jmva.2016.05.002
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    References listed on IDEAS

    as
    1. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    2. 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.
    3. 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.
    4. Joseph Ibrahim & Geert Molenberghs, 2009. "Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 1-43, May.
    5. Joseph Ibrahim & Geert Molenberghs, 2009. "Rejoinder on: Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 68-75, May.
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    Cited by:

    1. Zhu, Ziwei & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional principal component analysis with heterogeneous missingness," LSE Research Online Documents on Economics 117647, London School of Economics and Political Science, LSE Library.
    2. Wang, Xin & Kong, Lingchen & Wang, Liqun, 2024. "Estimation of sparse covariance matrix via non-convex regularization," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    3. Matthieu Stigler & David Lobell, 2020. "On the benefits of index insurance in US agriculture: a large-scale analysis using satellite data," Papers 2011.12544, arXiv.org, revised Nov 2021.
    4. Denis Belomestny & Mathias Trabs & Alexandre Tsybakov, 2017. "Sparse covariance matrix estimation in high-dimensional deconvolution," Working Papers 2017-25, Center for Research in Economics and Statistics.
    5. 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.

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