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Sparse estimation of high-dimensional correlation matrices

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  • Cui, Ying
  • Leng, Chenlei
  • Sun, Defeng

Abstract

Several attempts to estimate covariance matrices with sparsity constraints have been made. A convex optimization formulation for estimating correlation matrices as opposed to covariance matrices is proposed. An efficient accelerated proximal gradient algorithm is developed, and it is shown that this method gives a faster rate of convergence. An adaptive version of this approach is also discussed. Simulation results and an analysis of a cardiovascular microarray confirm its performance and usefulness.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:390-403
    DOI: 10.1016/j.csda.2014.10.001
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    References listed on IDEAS

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    Cited by:

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    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. Shaoxin Wang & Hu Yang & Chaoli Yao, 2019. "On the penalized maximum likelihood estimation of high-dimensional approximate factor model," Computational Statistics, Springer, vol. 34(2), pages 819-846, June.
    4. Huang Lin & Merete Eggesbø & Shyamal Das Peddada, 2022. "Linear and nonlinear correlation estimators unveil undescribed taxa interactions in microbiome data," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    5. Yang, Guangren & Liu, Yiming & Pan, Guangming, 2019. "Weighted covariance matrix estimation," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 82-98.
    6. Yue, Mu & Li, Jialiang & Cheng, Ming-Yen, 2019. "Two-step sparse boosting for high-dimensional longitudinal data with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 222-234.
    7. Chen, Shuo & Kang, Jian & Xing, Yishi & Zhao, Yunpeng & Milton, Donald K., 2018. "Estimating large covariance matrix with network topology for high-dimensional biomedical data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 82-95.
    8. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    9. Tianyu Cui & Francesco Caravelli & Cozmin Ududec, 2017. "Correlations and Clustering in Wholesale Electricity Markets," Papers 1710.11184, arXiv.org, revised Nov 2017.
    10. Vahe Avagyan & Andrés M. Alonso & Francisco J. Nogales, 2018. "D-trace estimation of a precision matrix using adaptive Lasso penalties," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 425-447, June.

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