Covariance estimation for distributions with \({2+\varepsilon}\) moments
From MaRDI portal
Publication:378788
DOI10.1214/12-AOP760zbMath1293.62121arXiv1106.2775OpenAlexW3099857106WikidataQ105585026 ScholiaQ105585026MaRDI QIDQ378788
Nikhil Srivastava, R. V. Vershinin
Publication date: 12 November 2013
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1106.2775
Stieltjes transformrandom matriceslog-concave distributionscovariance matriceshigh-dimensional distributions
Related Items
Coverings of random ellipsoids, and invertibility of matrices with i.i.d. heavy-tailed entries, Controlling the least eigenvalue of a random Gram matrix, On the interval of fluctuation of the singular values of random matrices, Sampling discretization and related problems, Concentration phenomena in high dimensional geometry, The smallest singular value of random rectangular matrices with no moment assumptions on entries, Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices, The relative effects of dimensionality and multiplicity of hypotheses on the \(F\)-test in linear regression, Unnamed Item, The lower tail of random quadratic forms with applications to ordinary least squares, On the convergence of the extremal eigenvalues of empirical covariance matrices with dependence, On Sufficient Conditions in the Marchenko--Pastur Theorem, Non-asymptotic bounds for the \(\ell_{\infty}\) estimator in linear regression with uniform noise, Dimension-free bounds for sums of independent matrices and simple tensors via the variational principle, Dimension-free bounds for sums of dependent matrices and operators with heavy-tailed distributions, Restricted Invertibility Revisited, Approximating the covariance ellipsoid, On the discrepancy of random matrices with many columns, Estimating covariance and precision matrices along subspaces, The spectral norm of random inner-product kernel matrices, On higher order isotropy conditions and lower bounds for sparse quadratic forms, The smallest singular value of a shifted $d$-regular random square matrix, The limit of the smallest singular value of random matrices with i.i.d. entries, Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries, Sparse recovery under weak moment assumptions, Generalized canonical correlation analysis for classification, Robust high-dimensional factor models with applications to statistical machine learning, On Monte-Carlo methods in convex stochastic optimization, Moment bounds for large autocovariance matrices under dependence, On the behaviour of the smallest eigenvalue of a high-dimensional sample covariance matrix, Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices, Quantitative Version of a Silverstein’s Result, Covariance estimation under one-bit quantization
Cites Work
- Unnamed Item
- The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
- Sharp bounds on the rate of convergence of the empirical covariance matrix
- Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
- How close is the sample covariance matrix to the actual covariance matrix?
- Concentration of mass on convex bodies
- A note on the largest eigenvalue of a large dimensional sample covariance matrix
- Random vectors in the isotropic position
- On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
- Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities
- Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
- Random walks and anO*(n5) volume algorithm for convex bodies
- Some estimates of norms of random matrices
- Twice-Ramanujan Sparsifiers