Electronic Journal of Statistics

Discussion of “Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation”

Hui Zou

Full-text: Open access

Abstract

Professors Cai, Ren and Zhou ought to be congratulated for writing such a wonderful expository paper on optimal estimation of high-dimensional covariance and precision matrices. Nearly all optimality results on large matrix estimation were established by the authors (and their co-authors). Thus, they are the most appropriate team to write this much needed review article. My discussion contains three sections.

Article information

Source
Electron. J. Statist., Volume 10, Number 1 (2016), 60-66.

Dates
Received: March 2015
First available in Project Euclid: 17 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1455715953

Digital Object Identifier
doi:10.1214/15-EJS1018

Mathematical Reviews number (MathSciNet)
MR3466173

Zentralblatt MATH identifier
1331.62281

Citation

Zou, Hui. Discussion of “Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation”. Electron. J. Statist. 10 (2016), no. 1, 60--66. doi:10.1214/15-EJS1018. https://projecteuclid.org/euclid.ejs/1455715953


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References

  • Fan, J., Xue, L. and Zou, H. (2014). Strong Oracle Optimality of Folded Concave Penalized Estimation., Annals of Statistics 42 819–849.
  • Li, D. and Zou, H. (2014). SURE Information Criteria for Large Covariance Matrix Estimation and Their Asymptotic Properties., arXiv:1406.6514.
  • Mai, Q. and Zou, H. (2015). Sparse Semiparametric Discriminant Analysis., Journal of Multivariate Analysis 135 175–188.
  • Xue, L. and Zou, H. (2012). Regularized Rank-based Estimation of High-dimensional Nonparanormal Graphical Models., Annals of Statistics 40 2541–2571.
  • Xue, L. and Zou, H. (2013). Optimal Estimation of Sparse Correlation Matrices of Semiparametric Gaussian Copulas., Statistics and Its Interface 7 201–209.
  • Xue, L. and Zou, H. (2014). Rank-based Tapering Estimation of Bandable Correlation Matrices., Statistica Sinica 24 83–100.
  • Yi, F. and Zou, H. (2013). SURE-tuned Tapering Estimation of Large Covariance Matrices., Computational Statisticsa and Data Analysis 58 339–351.

See also

  • Related item: T. Tony Cai, Zhao Ren, Harrison H. Zhou (2016). Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation. Electron. J. Statist. Vol. 10, Iss. 1, 1–59.