Adaptive Thresholding for Sparse Covariance Matrix EstimationTony Cai and Weidong Liu
Adaptive Thresholding for Sparse Covariance Matrix EstimationTony Cai and Weidong Liu
- Abstract: In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be sub-optimal over the same parameter spaces. Support recovery is also discussed. The adaptive thresholding estimators are easy to implement. Numerical performance of the estimators is studied using both simulated and real data. Simulation results show that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumors microarray experiment.
- Paper: pdf file.
- Supplement: This supplement contains additional technical proofs.
- Other related papers:
- Cai, T. & Zhou, H. (2010).
Optimal rates of convergence for sparse covariance matrix estimation.
Technical report.
- Cai, T., Zhang, C.-H. & Zhou, H. (2010).
Optimal rates of convergence for covariance matrix estimation
The Annals of Statistics 38, 2118-2144.
- Cai, T., Liu, W. & Luo, X. (2010).
A constrained l1 minimization approach to sparse precision matrix estimation
J. American Statistical Association 106, 594-607.
- Cai, T. & Zhou, H. (2009).
Minimax estimation of large covariance matrices under l1 norm (with discussion)
Statistica Sinica, to appear.