The Annals of Statistics, ISSN 0090-5364, 4/2010, Volume 38, Issue 2, pp. 894 - 942

We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is...

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 | REGRESSION | SPARSITY | penalized estimation | correct selection | DANTZIG SELECTOR | risk estimation | degrees of freedom | model selection | RISK | STATISTICS & PROBABILITY | selection consistency | sign consistency | nonconvex minimization | NONCONCAVE PENALIZED LIKELIHOOD | mean squared error | least squares | unbiasedness | ADAPTIVE LASSO | LARGER | minimax | STATISTICAL ESTIMATION | 62J05 | 62J07 | 62H12 | 62H25

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 | REGRESSION | SPARSITY | penalized estimation | correct selection | DANTZIG SELECTOR | risk estimation | degrees of freedom | model selection | RISK | STATISTICS & PROBABILITY | selection consistency | sign consistency | nonconvex minimization | NONCONCAVE PENALIZED LIKELIHOOD | mean squared error | least squares | unbiasedness | ADAPTIVE LASSO | LARGER | minimax | STATISTICAL ESTIMATION | 62J05 | 62J07 | 62H12 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 8/2008, Volume 36, Issue 4, pp. 1567 - 1594

Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436-1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood...

Regression coefficients | Variable coefficients | Linear regression | Eigenvalues | Neighborhood conditions | Mathematical vectors | Matrices | Coefficients | Covariance matrices | Estimators | High-dimensional data | Random matrices | Bias | Penalized regression | Spectral analysis | Rate consistency | Variable selection | DANTZIG SELECTOR | random matrices | high-dimensional data | bias | spectral analysis | RISK | STATISTICS & PROBABILITY | variable selection | rate consistency | penalized regression | LARGER | STATISTICAL ESTIMATION | 62J05 | 62J07 | 62H25

Regression coefficients | Variable coefficients | Linear regression | Eigenvalues | Neighborhood conditions | Mathematical vectors | Matrices | Coefficients | Covariance matrices | Estimators | High-dimensional data | Random matrices | Bias | Penalized regression | Spectral analysis | Rate consistency | Variable selection | DANTZIG SELECTOR | random matrices | high-dimensional data | bias | spectral analysis | RISK | STATISTICS & PROBABILITY | variable selection | rate consistency | penalized regression | LARGER | STATISTICAL ESTIMATION | 62J05 | 62J07 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2009, Volume 37, Issue 6B, pp. 4104 - 4130

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high....

Mathematical theorems | Sample size | Covariance | Data visualization | Eigenvalues | Principal components analysis | Eigenvectors | Random variables | Covariance matrices | Perceptron convergence procedure | Sample covariance matrix | ρ-mixing | High Dimension | Consistency and strong inconsistency | Nonstandard asymptotics | Principal Component Analysis | Low Sample Size data | Spiked population model | consistency and strong inconsistency | spiked population model | LARGEST EIGENVALUE | rho-mixing | nonstandard asymptotics | GEOMETRIC REPRESENTATION | STATISTICS & PROBABILITY | low sample size data | high dimension | sample covariance matrix | Principal component analysis | COVARIANCE MATRICES | 62F12 | 34L20 | 62H25

Mathematical theorems | Sample size | Covariance | Data visualization | Eigenvalues | Principal components analysis | Eigenvectors | Random variables | Covariance matrices | Perceptron convergence procedure | Sample covariance matrix | ρ-mixing | High Dimension | Consistency and strong inconsistency | Nonstandard asymptotics | Principal Component Analysis | Low Sample Size data | Spiked population model | consistency and strong inconsistency | spiked population model | LARGEST EIGENVALUE | rho-mixing | nonstandard asymptotics | GEOMETRIC REPRESENTATION | STATISTICS & PROBABILITY | low sample size data | high dimension | sample covariance matrix | Principal component analysis | COVARIANCE MATRICES | 62F12 | 34L20 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 6/2013, Volume 41, Issue 3, pp. 1055 - 1084

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We...

Minimax | Covariance | Threshing | Eigenvalues | Population estimates | Coordinate systems | Principal components analysis | Eigenvectors | Covariance matrices | Estimators | High-dimensional data | Spiked covariance model | Minimax risk | Sparsity | Principal component analysis | CONSISTENCY | RATES | APPROXIMATION | high-dimensional data | COVARIANCE-MATRIX ESTIMATION | CONVERGENCE | STATISTICS & PROBABILITY | sparsity | MODEL | spiked covariance model | principal component analysis | 62G20 | 62H25

Minimax | Covariance | Threshing | Eigenvalues | Population estimates | Coordinate systems | Principal components analysis | Eigenvectors | Covariance matrices | Estimators | High-dimensional data | Spiked covariance model | Minimax risk | Sparsity | Principal component analysis | CONSISTENCY | RATES | APPROXIMATION | high-dimensional data | COVARIANCE-MATRIX ESTIMATION | CONVERGENCE | STATISTICS & PROBABILITY | sparsity | MODEL | spiked covariance model | principal component analysis | 62G20 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2008, Volume 36, Issue 6, pp. 2791 - 2817

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of n observations (samples), each with p variables. In this paper,...

Statistical variance | Approximation | Covariance | Eigenvalues | Signal noise | Principal components analysis | Eigenvectors | Matrices | Random variables | Covariance matrices | Spiked covariance model | Random matrix theory | Matrix perturbation | Phase transition | Principal component analysis | matrix perturbation | LARGEST EIGENVALUE | random matrix theory | DIMENSIONAL RANDOM MATRICES | ROOTS | STATISTICS & PROBABILITY | phase transition | MODEL | spiked covariance model | EMPIRICAL DISTRIBUTION | COVARIANCE MATRICES | 15A42 | 62H25 | 62E17

Statistical variance | Approximation | Covariance | Eigenvalues | Signal noise | Principal components analysis | Eigenvectors | Matrices | Random variables | Covariance matrices | Spiked covariance model | Random matrix theory | Matrix perturbation | Phase transition | Principal component analysis | matrix perturbation | LARGEST EIGENVALUE | random matrix theory | DIMENSIONAL RANDOM MATRICES | ROOTS | STATISTICS & PROBABILITY | phase transition | MODEL | spiked covariance model | EMPIRICAL DISTRIBUTION | COVARIANCE MATRICES | 15A42 | 62H25 | 62E17

Journal Article

The Annals of Statistics, ISSN 0090-5364, 10/2009, Volume 37, Issue 5B, pp. 2877 - 2921

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance...

Sufficient conditions | Covariance | Sample size | Threshing | Eigenvalues | Principal components analysis | Eigenvectors | Matrices | Mathematical vectors | Covariance matrices | High-dimensional statistics | Random matrices | Semidefinite programming | Sparsity | Spiked covariance ensembles | Convex relaxation | Wishart ensembles | Spectral analysis | Principal component analysis | random matrices | spiked covariance ensembles | spectral analysis | STATISTICS & PROBABILITY | sparsity | semidefinite programming | NORM | high-dimensional statistics | convex relaxation | COVARIANCE | SELECTION | 62F12 | 62H25

Sufficient conditions | Covariance | Sample size | Threshing | Eigenvalues | Principal components analysis | Eigenvectors | Matrices | Mathematical vectors | Covariance matrices | High-dimensional statistics | Random matrices | Semidefinite programming | Sparsity | Spiked covariance ensembles | Convex relaxation | Wishart ensembles | Spectral analysis | Principal component analysis | random matrices | spiked covariance ensembles | spectral analysis | STATISTICS & PROBABILITY | sparsity | semidefinite programming | NORM | high-dimensional statistics | convex relaxation | COVARIANCE | SELECTION | 62F12 | 62H25

Journal Article

7.
Full Text
Properties of Principal Component Methods for Functional and Longitudinal Data Analysis

The Annals of Statistics, ISSN 0090-5364, 6/2006, Volume 34, Issue 3, pp. 1493 - 1517

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of "functional data...

Data analysis | Covariance | Eigenvalues | Eigenfunctions | Principal components analysis | Mathematical functions | Longitudinal data | Data smoothing | Estimators | Consistent estimators | Principal Component Methodology | Eigenvector | Eigenfunction | Eigenvalue | Operator theory | Curse of dimensionality | Local polynomial methods | Nonparametric | Biomedical studies | Optimal convergence rate | Karhunen-Loeve expansion | Rate of convergence | Semiparametric | Principal component analysis | local polynomial methods | spectral decomposition | sparse data | curse of dimensionality | semiparametric | eigenfunction | rate of convergence | STATISTICS & PROBABILITY | optimal convergence rate | INFERENCE | nonparametric | CURVES | eigenvector | RATES | biomedical studies | ESTIMATORS | CONVERGENCE | smoothing | LINEAR-MODEL | operator theory | eigenvalue | principal component analysis | 62G08 | 62M09 | Karhunen–Loève expansion | 62H25

Data analysis | Covariance | Eigenvalues | Eigenfunctions | Principal components analysis | Mathematical functions | Longitudinal data | Data smoothing | Estimators | Consistent estimators | Principal Component Methodology | Eigenvector | Eigenfunction | Eigenvalue | Operator theory | Curse of dimensionality | Local polynomial methods | Nonparametric | Biomedical studies | Optimal convergence rate | Karhunen-Loeve expansion | Rate of convergence | Semiparametric | Principal component analysis | local polynomial methods | spectral decomposition | sparse data | curse of dimensionality | semiparametric | eigenfunction | rate of convergence | STATISTICS & PROBABILITY | optimal convergence rate | INFERENCE | nonparametric | CURVES | eigenvector | RATES | biomedical studies | ESTIMATORS | CONVERGENCE | smoothing | LINEAR-MODEL | operator theory | eigenvalue | principal component analysis | 62G08 | 62M09 | Karhunen–Loève expansion | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 8/2011, Volume 39, Issue 4, pp. 1878 - 1915

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing...

Community structure | Algorithms | Spectral theory | Eigenvalues | Eigenvectors | Laplacians | Matrices | Stochastic models | Spectral graph theory | Perceptron convergence procedure | Latent space model | Principal components analysis | Convergence of eigenvectors | Spectral clustering | Stochastic Blockmodel | Clustering | ALGORITHM | STATISTICS & PROBABILITY | MODEL | latent space model | principal components analysis | PREDICTION | CONSISTENCY | SOCIAL NETWORK ANALYSIS | COMMUNITY STRUCTURE | DIRECTED-GRAPHS | EIGENVECTORS | convergence of eigenvectors | clustering | 62H30 | 60B20 | 62H25

Community structure | Algorithms | Spectral theory | Eigenvalues | Eigenvectors | Laplacians | Matrices | Stochastic models | Spectral graph theory | Perceptron convergence procedure | Latent space model | Principal components analysis | Convergence of eigenvectors | Spectral clustering | Stochastic Blockmodel | Clustering | ALGORITHM | STATISTICS & PROBABILITY | MODEL | latent space model | principal components analysis | PREDICTION | CONSISTENCY | SOCIAL NETWORK ANALYSIS | COMMUNITY STRUCTURE | DIRECTED-GRAPHS | EIGENVECTORS | convergence of eigenvectors | clustering | 62H30 | 60B20 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2013, Volume 41, Issue 2, pp. 772 - 801

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading...

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 | CONSISTENCY | thresholding | STATISTICS & PROBABILITY | sparsity | ASYMPTOTICS | principal subspace | high-dimensional statistics | spiked covariance model | principal component analysis | 62G20 | 62H12 | 62H25

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 | CONSISTENCY | thresholding | STATISTICS & PROBABILITY | sparsity | ASYMPTOTICS | principal subspace | high-dimensional statistics | spiked covariance model | principal component analysis | 62G20 | 62H12 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2013, Volume 41, Issue 6, pp. 3074 - 3110

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax...

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 | EIGENVALUE | thresholding | POWER METHOD | optimal rate of convergence | APPROXIMATION | PERTURBATION | COVARIANCE-MATRIX ESTIMATION | STATISTICS & PROBABILITY | aggregation | LOW-RANK MATRICES | covariance matrix | eigenvector | minimax lower bound | CONSISTENCY | CONVERGENCE | group sparsity | principal component analysis | HIGH DIMENSION | low-rank matrix | 62C20 | 62H12 | 62H25

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 | EIGENVALUE | thresholding | POWER METHOD | optimal rate of convergence | APPROXIMATION | PERTURBATION | COVARIANCE-MATRIX ESTIMATION | STATISTICS & PROBABILITY | aggregation | LOW-RANK MATRICES | covariance matrix | eigenvector | minimax lower bound | CONSISTENCY | CONVERGENCE | group sparsity | principal component analysis | HIGH DIMENSION | low-rank matrix | 62C20 | 62H12 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 8/2013, Volume 41, Issue 4, pp. 1780 - 1815

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test...

Minimax | Eigenvalues | Principal components analysis | Polynomials | Matrices | Random variables | Covariance matrices | Statistics | Probabilities | Unit vectors | Spiked covariance model | Semidefinite relaxation | Sparse principal component analysis | Minimax lower bounds | High-dimensional detection | Planted clique | SUBMATRICES | LARGEST EIGENVALUE | SIZE | STATISTICS & PROBABILITY | LARGE HIDDEN CLIQUE | sparse principal component analysis | spiked covariance model | planted clique | PCA | semidefinite relaxation | CONSISTENCY | minimax lower bounds | RELAXATIONS | MATRICES | NORM | NOISY | 90C22 | 62F04 | 62H25

Minimax | Eigenvalues | Principal components analysis | Polynomials | Matrices | Random variables | Covariance matrices | Statistics | Probabilities | Unit vectors | Spiked covariance model | Semidefinite relaxation | Sparse principal component analysis | Minimax lower bounds | High-dimensional detection | Planted clique | SUBMATRICES | LARGEST EIGENVALUE | SIZE | STATISTICS & PROBABILITY | LARGE HIDDEN CLIQUE | sparse principal component analysis | spiked covariance model | planted clique | PCA | semidefinite relaxation | CONSISTENCY | minimax lower bounds | RELAXATIONS | MATRICES | NORM | NOISY | 90C22 | 62F04 | 62H25

Journal Article

Biometrika, ISSN 0006-3444, 12/2017, Volume 104, Issue 4, pp. 901 - 922

Evolutionary relationships are represented by phylogenetic trees, and a phylogenetic analysis of gene sequences typically produces a collection of these trees,...

Fréchet mean | Phylogenetic tree | Tree space | Principal component analysis

Fréchet mean | Phylogenetic tree | Tree space | Principal component analysis

Journal Article

Journal of Multivariate Analysis, ISSN 0047-259X, 07/2018, Volume 166, pp. 1 - 16

In the analysis of data with high-dimensional covariates and small sample sizes, dimension reduction techniques have been extensively employed. Principal...

Integrative analysis | Sparse PCA | 62H25 | Contrasted penalization | CONSISTENCY | PENALIZATION | STATISTICS & PROBABILITY | MODEL | CANCER | HIGH DIMENSION | PCA

Integrative analysis | Sparse PCA | 62H25 | Contrasted penalization | CONSISTENCY | PENALIZATION | STATISTICS & PROBABILITY | MODEL | CANCER | HIGH DIMENSION | PCA

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2010, Volume 38, Issue 2, pp. 1194 - 1226

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most...

Data analysis | Covariance | Kernel functions | Eigenvalues | Eigenfunctions | Principal components analysis | Longitudinal data | Random variables | Data smoothing | Estimators | Sparse data | Smoothing | Functional data analysis | Local linear regression | Functional principal components analysis | Longitudinal data analysis | functional principal components analysis | local linear regression | sparse data | MODELS | ESTIMATORS | longitudinal data analysis | STATISTICS & PROBABILITY | smoothing | 62M15 | 62G20 | 62H25

Data analysis | Covariance | Kernel functions | Eigenvalues | Eigenfunctions | Principal components analysis | Longitudinal data | Random variables | Data smoothing | Estimators | Sparse data | Smoothing | Functional data analysis | Local linear regression | Functional principal components analysis | Longitudinal data analysis | functional principal components analysis | local linear regression | sparse data | MODELS | ESTIMATORS | longitudinal data analysis | STATISTICS & PROBABILITY | smoothing | 62M15 | 62G20 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2011, Volume 39, Issue 6, pp. 3320 - 3356

The variance-covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular...

Dimensionality | Covariance | Threshing | Mathematical vectors | Standard deviation | Covariance matrices | Estimators | Consistent estimators | Estimation methods | Econometric factor models | thresholding | SEEMINGLY UNRELATED REGRESSIONS | NUMBER | Sparse estimation | seemingly unrelated regression | idiosyncratic | common factors | STATISTICS & PROBABILITY | REGULARIZATION | cross-sectional correlation | 62F12 | 62H12 | 62H25 | sparse estimation

Dimensionality | Covariance | Threshing | Mathematical vectors | Standard deviation | Covariance matrices | Estimators | Consistent estimators | Estimation methods | Econometric factor models | thresholding | SEEMINGLY UNRELATED REGRESSIONS | NUMBER | Sparse estimation | seemingly unrelated regression | idiosyncratic | common factors | STATISTICS & PROBABILITY | REGULARIZATION | cross-sectional correlation | 62F12 | 62H12 | 62H25 | sparse estimation

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 05/2017, Volume 46, Issue 9, pp. 4599 - 4619

Confirmatory factor analysis (CFA) model is a useful multivariate statistical tool for interpreting relationships between latent variables and manifest...

confirmatory factor model | model comparison | truncated Dirichlet prior | 62H25; 62G07 | Blocked Gibbs sampler | NONPARAMETRIC PROBLEMS | 62G07 | MAXIMUM-LIKELIHOOD | SAMPLING METHODS | DENSITY-ESTIMATION | STATISTICS & PROBABILITY | MONTE-CARLO | MIXTURES | EM ALGORITHM | SELECTION | 62H25 | Economic models | Bayesian analysis | Discriminant analysis | Samplers | Heterogeneity | Mathematical analysis | Dirichlet problem | Distortion | Mathematical models | Statistics

confirmatory factor model | model comparison | truncated Dirichlet prior | 62H25; 62G07 | Blocked Gibbs sampler | NONPARAMETRIC PROBLEMS | 62G07 | MAXIMUM-LIKELIHOOD | SAMPLING METHODS | DENSITY-ESTIMATION | STATISTICS & PROBABILITY | MONTE-CARLO | MIXTURES | EM ALGORITHM | SELECTION | 62H25 | Economic models | Bayesian analysis | Discriminant analysis | Samplers | Heterogeneity | Mathematical analysis | Dirichlet problem | Distortion | Mathematical models | Statistics

Journal Article

The Annals of Statistics, ISSN 0090-5364, 2/2012, Volume 40, Issue 1, pp. 436 - 465

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater...

Maximum likelihood estimation | Factor analysis | Maximum likelihood estimators | Mathematical independent variables | Matrices | Covariance matrices | Estimators | Consistent estimators | Estimation methods | Econometric factor models | High-dimensional factor models | Factor loadings | Factors | Idiosyncratic variances | Principal components | idiosyncratic variances | RETURN | NUMBER | ESTIMATORS | STATISTICS & PROBABILITY | principal components | ARBITRAGE | maximum likelihood estimation | factors | factor loadings | 62F12 | 62H25

Maximum likelihood estimation | Factor analysis | Maximum likelihood estimators | Mathematical independent variables | Matrices | Covariance matrices | Estimators | Consistent estimators | Estimation methods | Econometric factor models | High-dimensional factor models | Factor loadings | Factors | Idiosyncratic variances | Principal components | idiosyncratic variances | RETURN | NUMBER | ESTIMATORS | STATISTICS & PROBABILITY | principal components | ARBITRAGE | maximum likelihood estimation | factors | factor loadings | 62F12 | 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 2/2009, Volume 37, Issue 1, pp. 1 - 34

Functional principal component analysis (FPCA) based on the Karhunen-Loève decomposition has been successfully applied in many applications, mainly for one...

Statistical variance | Data analysis | Covariance | Eigenvalues | Eigenfunctions | Inference | Principal components analysis | Random variables | Estimators | Estimation methods | Functional principal components | Bootstrap | Two sample problem | Nonparametric regression | nonparametric regression | STATISTICS & PROBABILITY | LONGITUDINAL DATA | bootstrap | INFERENCE | CURVES | two sample problem | 62G08 | 62P05 | 62H25

Statistical variance | Data analysis | Covariance | Eigenvalues | Eigenfunctions | Inference | Principal components analysis | Random variables | Estimators | Estimation methods | Functional principal components | Bootstrap | Two sample problem | Nonparametric regression | nonparametric regression | STATISTICS & PROBABILITY | LONGITUDINAL DATA | bootstrap | INFERENCE | CURVES | two sample problem | 62G08 | 62P05 | 62H25

Journal Article

Annals of Statistics, ISSN 0090-5364, 10/2017, Volume 45, Issue 5, pp. 1863 - 1894

We consider large-scale studies in which thousands of significance tests are performed simultaneously. In some of these studies, the multiple testing procedure...

Unwanted variation | Robust regression | Batch effect | Empirical null | Surrogate variable analysis | surrogate variable analysis | REGRESSION | GENOMIC DATA | NUMBER | unwanted variation | CAUSAL INFERENCE | CORRELATED Z-VALUES | STATISTICS & PROBABILITY | DEPENDENCE | FALSE DISCOVERY RATE | batch effect | robust regression | GENE-EXPRESSION | FACTOR MODELS | MICROARRAY DATA | Primary 62J15 | secondary 62H25

Unwanted variation | Robust regression | Batch effect | Empirical null | Surrogate variable analysis | surrogate variable analysis | REGRESSION | GENOMIC DATA | NUMBER | unwanted variation | CAUSAL INFERENCE | CORRELATED Z-VALUES | STATISTICS & PROBABILITY | DEPENDENCE | FALSE DISCOVERY RATE | batch effect | robust regression | GENE-EXPRESSION | FACTOR MODELS | MICROARRAY DATA | Primary 62J15 | secondary 62H25

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2013, Volume 41, Issue 6, pp. 2905 - 2947

We study sparse principal components analysis in high dimensions, where p (the number of variables) can be much larger than n (the number of observations), and...

Minimax | Covariance | Analytical estimating | Principal components analysis | Eigenvectors | Matrices | Mathematical vectors | Covariance matrices | Estimators | Estimation methods | Highdimensional statistics | Random matrices | Minimax bounds | Sparsity | Subspace estimation | REGRESSION | random matrices | APPROXIMATION | STATISTICS & PROBABILITY | sparsity | COMPONENT ANALYSIS | MODEL | minimax bounds | VARIABLE SELECTION | PCA | CONSISTENCY | LASSO | subspace estimation | high-dimensional statistics | 62C20 | 62H12 | 62H25

Minimax | Covariance | Analytical estimating | Principal components analysis | Eigenvectors | Matrices | Mathematical vectors | Covariance matrices | Estimators | Estimation methods | Highdimensional statistics | Random matrices | Minimax bounds | Sparsity | Subspace estimation | REGRESSION | random matrices | APPROXIMATION | STATISTICS & PROBABILITY | sparsity | COMPONENT ANALYSIS | MODEL | minimax bounds | VARIABLE SELECTION | PCA | CONSISTENCY | LASSO | subspace estimation | high-dimensional statistics | 62C20 | 62H12 | 62H25

Journal Article

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