MINIMAX ESTIMATION OF LARGE COVARIANCE MATRICES UNDER ℓ1-NORM

By Tommaso Cai, Harrison H. Zhou. 2012

135 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/18ec199b601e3babc4cae6caeebeba21756e6cee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jianqing Fan
2. Tommaso Cai
3. Lingzhou Xue
4. Hui Zou
5. Harrison H. Zhou
6. Zhao Ren
7. Xiaohong Chen
8. Yazhen Wang

In Statistics and Probability

1. Tommaso Cai
2. Jianqing Fan
3. Harrison H. Zhou
4. Lingzhou Xue
5. Zhao Ren
6. Hui Zou
7. Victor Chernozhukov
8. Wei Biao Wu

Citations in the corpus

• Covariance and precision matrix estimation for high-dimensional time series (2013, background): “In contrast to the longstanding progresses and extensive research that have been made in terms of heuristics and methodology, theoretical work on estimation of covariance matrices based on high-dimensional time series data is largely untouched.”
• FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA (2013, methodology): “For estimating the large sparse covariance matrix of Gaussian data, Bickel and Levina (2008) constructed a threshold estimator that can achieve con- vergence rate π(p) [ n−1/2 log1/2 p ]1−δ , and Cai and Zhou (2012, 2013) showed that such a convergence rate is optimal.”
• Multitask Quantile Regression under the Transnormal Model (2016, methodology): “Both the rank-based estimator ˆ (cid:2) s 1 and its “oracle” counterpart achieve the minimax optimal convergence rate under the matrix (cid:2) 1 norm (Cai and Zhou 2012).”
• Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “See Cai and Zhou (2012b).”
• Random matrix theory in statistics: A review (2014, background): “Cai and Zhou (2012a) proved the minimax rates for the thresholding estimator in terms of the matrix l1 norm loss over the same class.”
• Adaptive Thresholding for Sparse Covariance Matrix Estimation (2011, unknown): “Cai and Zhou (2009, 2010) established the minimax rates of convergence under the matrix 1 norm and the spectral norm.”
• The spectral norm of random inner-product kernel matrices (2015, background): “Optimal rates of convergence under various matrix norms and sparsity models were established in [15, 14], and generalizations to other thresholding functions and to “adaptive” entryspecific thresholds were studied respectively in [46] and [11].”