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Ridge estimation of inverse covariance matrices from high-dimensional data

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  • van Wieringen, Wessel N.
  • Peeters, Carel F.W.

Abstract

The ridge estimation of the precision matrix is investigated in the setting where the number of variables is large relative to the sample size. First, two archetypal ridge estimators are reviewed and it is noted that their penalties do not coincide with common quadratic ridge penalties. Subsequently, starting from a proper ℓ2-penalty, analytic expressions are derived for two alternative ridge estimators of the precision matrix. The alternative estimators are compared to the archetypes with regard to eigenvalue shrinkage and risk. The alternatives are also compared to the graphical lasso within the context of graphical modeling. The comparisons may give reason to prefer the proposed alternative estimators.

Suggested Citation

  • van Wieringen, Wessel N. & Peeters, Carel F.W., 2016. "Ridge estimation of inverse covariance matrices from high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 284-303.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:284-303
    DOI: 10.1016/j.csda.2016.05.012
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    Cited by:

    1. Azam Kheyri & Andriette Bekker & Mohammad Arashi, 2022. "High-Dimensional Precision Matrix Estimation through GSOS with Application in the Foreign Exchange Market," Mathematics, MDPI, vol. 10(22), pages 1-19, November.
    2. van Wieringen, Wessel N. & Stam, Koen A. & Peeters, Carel F.W. & van de Wiel, Mark A., 2020. "Updating of the Gaussian graphical model through targeted penalized estimation," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    3. Jiadong Ji & Yong He & Lei Liu & Lei Xie, 2021. "Brain connectivity alteration detection via matrix‐variate differential network model," Biometrics, The International Biometric Society, vol. 77(4), pages 1409-1421, December.
    4. Vahe Avagyan, 2022. "Precision matrix estimation using penalized Generalized Sylvester matrix equation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 950-967, December.
    5. van Wieringen, Wessel N., 2017. "On the mean squared error of the ridge estimator of the covariance and precision matrix," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 88-92.
    6. Mehran Aflakparast & Mathisca de Gunst & Wessel van Wieringen, 2020. "Analysis of Twitter data with the Bayesian fused graphical lasso," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-28, July.
    7. Carel F. W. Peeters & Mark A. Wiel & Wessel N. Wieringen, 2020. "The spectral condition number plot for regularization parameter evaluation," Computational Statistics, Springer, vol. 35(2), pages 629-646, June.
    8. Wessel N. van Wieringen & Carel F. W. Peeters & Renee X. de Menezes & Mark A. van de Wiel, 2018. "Testing for pathway (in)activation by using Gaussian graphical models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1419-1436, November.

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