Adaptive covariance matrix estimation through block thresholding

DOI10.1214/12-AOS999zbMath1257.62060arXiv1211.0459OpenAlexW2078038009MaRDI QIDQ1940765

Ming Yuan, T. Tony Cai

Publication date: 7 March 2013

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0459

zbMATH Keywords

Frobenius normadaptive estimationminimax estimationoptimal rate of convergencespectral normblock thresholding

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Minimax procedures in statistical decision theory (62C20)

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Uses Software

• glasso

Cites Work

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• Sparse inverse covariance estimation with the graphical lasso
• A well-conditioned estimator for large-dimensional covariance matrices
• High dimensional covariance matrix estimation using a factor model
• Optimal rates of convergence for sparse covariance matrix estimation
• Optimal rates of convergence for covariance matrix estimation
• Covariance regularization by thresholding
• Operator norm consistent estimation of large-dimensional sparse covariance matrices
• Sparsistency and rates of convergence in large covariance matrix estimation
• Adaptive wavelet estimation: A block thresholding and oracle inequality approach
• Adaptive estimation of a quadratic functional by model selection.
• Sparse permutation invariant covariance estimation
• High-dimensional covariance estimation by minimizing \(\ell _{1}\)-penalized log-determinant divergence
• Regularized estimation of large covariance matrices
• A Constrainedℓ₁Minimization Approach to Sparse Precision Matrix Estimation
• Adaptive Thresholding for Sparse Covariance Matrix Estimation
• Model selection and estimation in the Gaussian graphical model
• Nonparametric Estimation of a Density of Unknown Smoothness
• Generalized Thresholding of Large Covariance Matrices
• Covariance matrix selection and estimation via penalised normal likelihood