Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries

DOI10.1214/17-AOS1642zbMath1418.62235arXiv1605.07129MaRDI QIDQ1991680

Stanislav Minsker

Publication date: 30 October 2018

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

Full work available at URL: https://arxiv.org/abs/1605.07129

zbMATH Keywords

matrix completionheavy tailsrandom matrixconcentration inequalitycovariance estimation

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Nonparametric robustness (62G35) Random matrices (probabilistic aspects) (60B20) Statistics of extreme values; tail inference (62G32) Random matrices (algebraic aspects) (15B52)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Geometric median and robust estimation in Banach spaces
• Marčenko-Pastur law for Tyler's M-estimator
• Covariance estimation for distributions with \({2+\varepsilon}\) moments
• High-dimensional covariance matrix estimation with missing observations
• Concentration inequalities and moment bounds for sample covariance operators
• Sub-Gaussian mean estimators
• On the estimation of the mean of a random vector
• Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
• Robust matrix completion
• User-friendly tail bounds for sums of random matrices
• Empirical risk minimization for heavy-tailed losses
• High-breakdown robust multivariate methods
• Optimal rates of convergence for covariance matrix estimation
• Sparsistency and rates of convergence in large covariance matrix estimation
• Random generation of combinatorial structures from a uniform distribution
• A distribution-free M-estimator of multivariate scatter
• The asymptotics of Rousseeuw's minimum volume ellipsoid estimator
• Robust m-estimators of multivariate location and scatter
• Asymptotics for the minimum covariance determinant estimator
• New asymptotic results in principal component analysis
• Challenging the empirical mean and empirical variance: a deviation study
• Convex trace functions and the Wigner-Yanase-Dyson conjecture
• Operator Lipschitz functions
• Robust principal component analysis?
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• Strong converse for identification via quantum channels
• An Introduction to Matrix Concentration Inequalities
• Robust Estimation of a Location Parameter
• Robust Statistics
• Estimating structured high-dimensional covariance and precision matrices: optimal rates and adaptive estimation

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