Adaptive Thresholding for Sparse Covariance Matrix Estimation
Tony Cai and Weidong Liu
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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., Zhang, C.-H. & Zhou, H. (2010).
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