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1. Full Text NEARLY UNBIASED VARIABLE SELECTION UNDER MINIMAX CONCAVE PENALTY
by Cun-Hui Zhang
The Annals of statistics, ISSN 0090-5364, 4/2010, Volume 38, Issue 2, pp. 894 - 942
Minimax | Degrees of freedom | Estimation bias | Unbiased estimators | Convexity | Computational complexity | Estimators | Concavity | Vertices | Oracles | Model selection | Nonconvex minimization | Sign consistency | Penalized estimation | Selection consistency | Correct selection | Risk estimation | Unbiasedness | Least squares | Mean squared error | Variable selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | General topics | Linear inference, regression | Decision theory | Exact sciences and technology | Probability and statistics | Statistics | Parametric inference | Sciences and techniques of general use | Studies | Algorithms | Regression analysis | Bias | penalized estimation | correct selection | 62J05 | 62J07 | risk estimation | degrees of freedom | model selection | selection consistency | sign consistency | nonconvex minimization | mean squared error | least squares | unbiasedness | 62H12 | minimax | 62H25
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2. Full Text Covariance Regularization by Thresholding
by Peter J. Bickel and Elizaveta Levina
The Annals of statistics, ISSN 0090-5364, 12/2008, Volume 36, Issue 6, pp. 2577 - 2604
Covariance | Threshing | Eigenvalues | Principal components analysis | Eigenvectors | Covariance matrices | Talus slopes | Estimators | Consistent estimators | Oracles | Large p small n | Sparsity | High dimension low sample size | Regularization | Thresholding | Covariance estimation | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Variables | Statistical analysis | Matrix | Estimates | large p small n | thresholding | 62G09 | regularization | high dimension low sample size | sparsity | 62F12 | 62H12
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3. Full Text ESTIMATING SPARSE PRECISION MATRIX: OPTIMAL RATES OF CONVERGENCE AND ADAPTIVE ESTIMATION
by T. Tony Cai and Weidong Liu and Harrison H. Zhou
The Annals of statistics, ISSN 0090-5364, 4/2016, Volume 44, Issue 2, pp. 455 - 488
Minimax | Mathematical procedures | Covariance | Threshing | Population estimates | Matrices | Random variables | Covariance matrices | Estimators | Estimation methods | Graphical model | Precision matrix | Constrained â„“1-minimization | Spectral norm | Sparsity | Optimal rate of convergence | Covariance matrix | Minimax lower bound | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Parameter estimation | Matrix | Numerical analysis | Estimating techniques | Multivariate analysis | minimax lower bound | optimal rate of convergence | spectral norm | 62G09 | graphical model | sparsity | 62F12 | 62H12 | Constrained \ell_{1}-minimization | precision matrix | covariance matrix
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4. Full Text NOISY MATRIX DECOMPOSITION VIA CONVEX RELAXATION: OPTIMAL RATES IN HIGH DIMENSIONS
by Alekh Agarwal and Sahand Negahban and Martin J. Wainwright
The Annals of statistics, ISSN 0090-5364, 4/2012, Volume 40, Issue 2, pp. 1171 - 1197
Factor analysis | Covariance | Error bounds | Principal components analysis | Matrices | Mathematical vectors | Convexity | Covariance matrices | Modeling | Estimators | High-dimensional inference | Composite regularizers | Nuclear norm | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Matrix | Stochastic models | Convex analysis | composite regularizers | nuclear norm | 62H12 | 62F30
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5. Full Text Regularized Estimation of Large Covariance Matrices
by Peter J. Bickel and Elizaveta Levina
The Annals of statistics, ISSN 0090-5364, 2/2008, Volume 36, Issue 1, pp. 199 - 227
Approximation | Covariance | Spectral energy distribution | Eigenvalues | Population estimates | White noise | Traffic estimation | Covariance matrices | Estimators | Oracles | Cholesky decomposition | Banding | Covariance matrix | Regularization | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | General topics | Distribution theory | Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) | Exact sciences and technology | Probability theory and stochastic processes | Probability and statistics | Statistics | Parametric inference | Sciences and techniques of general use | Studies | Regularization methods | Mathematical models | Matrix | Estimating techniques | Normal distribution | 62G09 | regularization | banding | 62F12 | 62H12
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6. Full Text Sparse permutation invariant covariance estimation
by Rothman, Adam J and Bickel, Peter J and Levina, Elizaveta and Zhu, Ji
Electronic journal of statistics, ISSN 1935-7524, 2008, Volume 2, pp. 494 - 515
Cholesky decomposition | Covariance matrix | Large p small n | Sparsity | High dimension low sample size | Lasso | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology
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7. Full Text Operator Norm Consistent Estimation of Large-Dimensional Sparse Covariance Matrices
by Noureddine El Karoui
The Annals of statistics, ISSN 0090-5364, 12/2008, Volume 36, Issue 6, pp. 2717 - 2756
Covariance | Spectral theory | Threshing | Eigenvalues | Population estimates | Adjacency matrix | Matrices | Covariance matrices | Estimators | Consistent estimators | Eigenvalues of covariance matrices | Random matrix theory | Multivariate statistical analysis | Sparsity | Adjacency matrices | β-sparsity | High-dimensional inference | Correlation matrices | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Variables | Matrix | Multivariate analysis | Estimates | adjacency matrices | high-dimensional inference | correlation matrices | eigenvalues of covariance matrices | random matrix theory | sparsity | 62H12 | multivariate statistical analysis
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8. Full Text Efficiency of the MLE in a multivariate parallel profile model with random effects
by Yokoyama Takahisa
Hiroshima mathematical journal, ISSN 0018-2079, 07/2005, Volume 35, Issue 2, pp. 197 - 203 @RTYE Article
62H12
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9. Full Text CONFIDENCE SETS FOR PERSISTENCE DIAGRAMS
by Brittany Terese Fasy and Fabrizio Lecci and Alessandro Rinaldo and Larry Wasserman and Sivaraman Balakrishnan and Aarti Singh
The Annals of statistics, ISSN 0090-5364, 12/2014, Volume 42, Issue 6, pp. 2301 - 2339
Density estimation | Diagrams | Bar codes | Signal noise | Mathematics | Topology | Estimators | Computational topology | Distance functions | Confidence interval | Persistent homology | Statistics & Probability | Physical Sciences | Science & Technology | Studies | Statistical methods | Topological manifolds | 62G05 | 62G20 | density estimation | 62H12 | topology
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10. Full Text LATENT VARIABLE GRAPHICAL MODEL SELECTION VIA CONVEX OPTIMIZATION
by Venkat Chandrasekaran and Pablo A. Parrilo and Alan S. Willsky
The Annals of statistics, ISSN 0090-5364, 8/2012, Volume 40, Issue 4, pp. 1935 - 1967
Tangents | Identifiability | Algebra | Covariance | Marginalization | Covariance matrices | Parametric models | Curvature | Consistent estimators | Fisher information | Gaussian graphical models | Sparsity | High-dimensional asymptotics | Latent variables | Low-rank | Algebraic statistics | Covariance selection | Regularization | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Statistical methods | Matrix | Random variables | Normal distribution | algebraic statistics | latent variables | covariance selection | regularization | low-rank | high-dimensional asymptotics | sparsity | 62F12 | 62H12
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11. Full Text SPARSE PCA: OPTIMAL RATES AND ADAPTIVE ESTIMATION
by T. Tony Cai and Zongming Ma and Yihong Wu
The Annals of statistics, ISSN 0090-5364, 12/2013, Volume 41, Issue 6, pp. 3074 - 3110
Aggregation | Preliminary estimates | Minimax | Approximation | Threshing | Principal components analysis | Eigenvectors | Covariance matrices | Estimators | Oracles | Group sparsity | Eigenvector | Optimal rate of convergence | Thresholding | Low-rank matrix | Adaptive estimation | Covariance matrix | Minimax lower bound | Principal component analysis | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Mathematical problems | Studies | Parameter estimation | Estimating techniques | Regression analysis | thresholding | optimal rate of convergence | aggregation | covariance matrix | eigenvector | minimax lower bound | 62C20 | 62H12 | group sparsity | principal component analysis | low-rank matrix | 62H25
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12. Full Text Propagation of Outliers in Multivariate Data
by Fatemah Alqallaf and Stefan Van Aelst and Victor J. Yohai and Ruben H. Zamar
The Annals of statistics, ISSN 0090-5364, 2/2009, Volume 37, Issue 1, pp. 311 - 331
Outliers | Componentwise operations | Histograms | Estimation bias | Infinity | Covariance | Matrices | Grants | Estimators | Point estimators | Contamination model | Influence function | Robustness | Independent contamination | Breakdown point | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | General topics | Exact sciences and technology | Probability and statistics | Multivariate analysis | Statistics | Sciences and techniques of general use | Studies | Measurement errors | Statistical methods | Estimating techniques | Contamination | contamination model | independent contamination | robustness | 62F35 | influence function | 62H12
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13. Full Text SPARSE PRINCIPAL COMPONENT ANALYSIS AND ITERATIVE THRESHOLDING
by Zongming Ma
The Annals of statistics, ISSN 0090-5364, 4/2013, Volume 41, Issue 2, pp. 772 - 801
Threshing | Eigenvalues | Principal components analysis | Coordinate systems | Eigenvectors | Covariance matrices | Estimators | Consistent estimators | Oracles | Estimation methods | Dimension reduction | High-dimensional statistics | Sparsity | Thresholding | Spiked covariance model | Principal component analysis | Principal subspace | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Random variables | Sample size | Iterative methods | thresholding | 62G20 | sparsity | principal subspace | high-dimensional statistics | spiked covariance model | 62H12 | principal component analysis | 62H25
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14. Full Text NONLINEAR SHRINKAGE ESTIMATION OF LARGE-DIMENSIONAL COVARIANCE MATRICES
by Olivier Ledoit and Michael Wolf
The Annals of statistics, ISSN 0090-5364, 4/2012, Volume 40, Issue 2, pp. 1024 - 1060
Monte Carlo methods | Sample size | Eigenvalues | Population estimates | Eigenvectors | Covariance matrices | Rotation | Estimators | Consistent estimators | Oracles | Rotation equivariance | Large-dimensional asymptotics | Nonlinear shrinkage | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Matrix | Nonlinear programming | Monte Carlo simulation | 15A52 | 62G20 | rotation equivariance | nonlinear shrinkage | 62H12
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15. Full Text Dimension Reduction for Nonelliptically Distributed Predictors
by Bing Li and Yuexiao Dong
The Annals of statistics, ISSN 0090-5364, 6/2009, Volume 37, Issue 3, pp. 1272 - 1298
Dimensionality reduction | Objective functions | Scatter plots | Linear regression | Matrices | Mathematical vectors | Mathematical functions | Parameterization | Estimators | Estimation methods | Kernel inverse regression | Parametric inverse regression | Central solution spaces | Inverse regression | Canonical correlation | Sliced inverse regression | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | General topics | Distribution theory | Exact sciences and technology | Probability theory and stochastic processes | Probability and statistics | Multivariate analysis | Statistics | Sciences and techniques of general use | Studies | Estimating techniques | Simulation | Asymptotic methods | parametric inverse regression | central solution spaces | 62G08 | 62G09 | inverse regression | sliced inverse regression | kernel inverse regression | 62H12
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16. Full Text VAST VOLATILITY MATRIX ESTIMATION FOR HIGH-FREQUENCY FINANCIAL DATA
by Yazhen Wang and Jian Zou
The Annals of statistics, ISSN 0090-5364, 4/2010, Volume 38, Issue 2, pp. 943 - 978
Brownian motion | Information retrieval noise | Price volatility | Threshing | Eigenvalues | Matrices | Financial data | Covariance matrices | Estimators | Estimation methods | Realized volatility | Sparsity | Microstructure noise | Integrated volatility | Convergence rate | Matrix norm | Diffusion | Regularization | Threshold | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | General topics | Applications | Insurance, economics, finance | Exact sciences and technology | Probability theory and stochastic processes | Markov processes | Probability and statistics | Sampling theory, sample surveys | Statistics | Sciences and techniques of general use | Studies | Prices | Theory | Volatility | 62G05 | integrated volatility | diffusion | 62P20 | 62M05 | regularization | realized volatility | sparsity | threshold | micro-structure noise | matrix norm | 62H12
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17. Full Text ASYMPTOTIC NORMALITY AND OPTIMALITIES IN ESTIMATION OF LARGE GAUSSIAN GRAPHICAL MODELS
by Zhao Ren and Tingni Sun and Cun-Hui Zhang and Harrison H. Zhou
The Annals of statistics, ISSN 0090-5364, 6/2015, Volume 43, Issue 3, pp. 991 - 1026
Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Regression analysis | Sample size | Normal distribution | Asymptotic methods | inference | optimal rate of convergence | spectral norm | 62G09 | scaled lasso | sparsity | Asymptotic efficiency | precision matrix | covariance matrix | minimax lower bound | latent graphical model | graphical model | 62F12 | 62H12
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