2006, Foundations and trends in communications and information theory, ISBN 1933019239, Volume 2, issue 3 (2006)., Issue v 2 3, 155-239, ix, 93

The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely...

Toeplitz matrices | Matrices | Theorems (Mathematics) | Research | Mathematical research | Analysis of covariance

Toeplitz matrices | Matrices | Theorems (Mathematics) | Research | Mathematical research | Analysis of covariance

Book

IEEE Transactions on Signal Processing, ISSN 1053-587X, 11/2014, Volume 62, Issue 22, pp. 6059 - 6070

In this paper, a general class of regularized M-estimators of scatter matrix are proposed that are suitable also for low or insufficient sample support (small...

Maximum likelihood estimation | Symmetric matrices | regularization | robustness | Covariance matrices | Equations | Geodesic convexity | complex elliptically symmetric distributions | M -estimator of scatter | Cost function | normalized matched filter | Convex functions | High definition video | M$-estimator of scatter | M-estimator of scatter | CONVEXITY | SUBSPACE DETECTORS | MULTIVARIATE LOCATION | ENGINEERING, ELECTRICAL & ELECTRONIC | CFAR DETECTION | COVARIANCE-MATRIX | MODELS | GAUSSIAN DISTRIBUTION | Signal processing | Usage | Mathematical optimization | Iterative methods (Mathematics) | Least squares | Innovations | Mathematical analysis | Radar detection | Uniqueness | Exact solutions | Transaction processing | Scatter | Estimators | Convergence

Maximum likelihood estimation | Symmetric matrices | regularization | robustness | Covariance matrices | Equations | Geodesic convexity | complex elliptically symmetric distributions | M -estimator of scatter | Cost function | normalized matched filter | Convex functions | High definition video | M$-estimator of scatter | M-estimator of scatter | CONVEXITY | SUBSPACE DETECTORS | MULTIVARIATE LOCATION | ENGINEERING, ELECTRICAL & ELECTRONIC | CFAR DETECTION | COVARIANCE-MATRIX | MODELS | GAUSSIAN DISTRIBUTION | Signal processing | Usage | Mathematical optimization | Iterative methods (Mathematics) | Least squares | Innovations | Mathematical analysis | Radar detection | Uniqueness | Exact solutions | Transaction processing | Scatter | Estimators | Convergence

Journal Article

2015, Cambridge series in statistical and probabilistic mathematics, ISBN 1107065178, xiv, 308

High-dimensional data appear in many fields, and their analysis has become increasingly important in modern statistics. However, it has long been observed that...

Multivariate analysis | Analysis of covariance | Statistics

Multivariate analysis | Analysis of covariance | Statistics

Book

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 10/2014, Volume 36, Issue 10, pp. 2047 - 2060

We extend kernelized matrix factorization with a full-Bayesian treatment and with an ability to work with multiple side information sources expressed as...

Automatic relevance determination | matrix factorization | multiple output regression | Computational modeling | biological interaction networks | Probabilistic logic | Approximation methods | variational approximation | Covariance matrices | multiple kernel learning | multilabel classification | Prediction algorithms | large margin learning | Bayes methods | Kernel | ALGORITHM | NETWORKS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Protein Interaction Mapping - methods | Data Interpretation, Statistical | Algorithms | Numerical Analysis, Computer-Assisted | Computer Simulation | Bayes Theorem | Models, Statistical | Machine Learning | Pattern Recognition, Automated - methods | Bayesian statistical decision theory | Usage | Kernel functions | Machine learning | Innovations | Approximation theory | Distribution (Probability theory) | Regression analysis | Methods | Entropy | Classification | Cell cycle | Kernels | State of the art | Data sets | Regression | Factorization | Information sources

Automatic relevance determination | matrix factorization | multiple output regression | Computational modeling | biological interaction networks | Probabilistic logic | Approximation methods | variational approximation | Covariance matrices | multiple kernel learning | multilabel classification | Prediction algorithms | large margin learning | Bayes methods | Kernel | ALGORITHM | NETWORKS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Protein Interaction Mapping - methods | Data Interpretation, Statistical | Algorithms | Numerical Analysis, Computer-Assisted | Computer Simulation | Bayes Theorem | Models, Statistical | Machine Learning | Pattern Recognition, Automated - methods | Bayesian statistical decision theory | Usage | Kernel functions | Machine learning | Innovations | Approximation theory | Distribution (Probability theory) | Regression analysis | Methods | Entropy | Classification | Cell cycle | Kernels | State of the art | Data sets | Regression | Factorization | Information sources

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 12/2013, Volume 61, Issue 23, pp. 5807 - 5818

In Abramovich ["Bounds on Maximum Likelihood Ratio-Part I: Application to Antenna Array Detection-Estimation With Perfect Wavefront Coherence," IEEE Trans....

Maximum likelihood estimation | Direction-of-arrival estimation | likelihood ratio | Training data | elliptically symmetric distributions | regularization | expected likelihood | Multiple signal classification | Covariance matrix estimation | Covariance matrices | Clutter | EXISTENCE | MUSIC | MAXIMUM-LIKELIHOOD | PERFORMANCE | SCATTER | ALGORITHM ANALYSIS | ARRAYS | ENGINEERING, ELECTRICAL & ELECTRONIC | MODELS | FRAMEWORK | COMPOUND-GAUSSIAN CLUTTER | Gaussian distribution | Signal processing | Usage | Statistical models | Maximum likelihood estimates (Statistics) | Innovations | Econometrics | Normal distribution | Estimating techniques | Samples | Detectors | Mathematical models | Statistical methods | Covariance matrix | Invariance | Estimates | Engineering Sciences | Computer Science | Signal and Image processing

Maximum likelihood estimation | Direction-of-arrival estimation | likelihood ratio | Training data | elliptically symmetric distributions | regularization | expected likelihood | Multiple signal classification | Covariance matrix estimation | Covariance matrices | Clutter | EXISTENCE | MUSIC | MAXIMUM-LIKELIHOOD | PERFORMANCE | SCATTER | ALGORITHM ANALYSIS | ARRAYS | ENGINEERING, ELECTRICAL & ELECTRONIC | MODELS | FRAMEWORK | COMPOUND-GAUSSIAN CLUTTER | Gaussian distribution | Signal processing | Usage | Statistical models | Maximum likelihood estimates (Statistics) | Innovations | Econometrics | Normal distribution | Estimating techniques | Samples | Detectors | Mathematical models | Statistical methods | Covariance matrix | Invariance | Estimates | Engineering Sciences | Computer Science | Signal and Image processing

Journal Article

6.
Full Text
HIGH-DIMENSIONAL SEMIPARAMETRIC ESTIMATE OF LATENT COVARIANCE MATRIX FOR MATRIX-VARIATE

STATISTICA SINICA, ISSN 1017-0405, 07/2019, Volume 29, Issue 3, pp. 1535 - 1559

Estimating the covariance matrix of a high-dimensional matrix-variate is an important issue. As such, many methods have been developed, typically based on the...

Kronecker product | STATISTICS & PROBABILITY | latent covariance (correlation) matrix | matrix-variate | robust estimate | KENDALLS TAU

Kronecker product | STATISTICS & PROBABILITY | latent covariance (correlation) matrix | matrix-variate | robust estimate | KENDALLS TAU

Journal Article

The Annals of Statistics, ISSN 0090-5364, 2/2015, Volume 43, Issue 1, pp. 177 - 214

Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original...

Latent space model | Sochastic blockmodel | Low rank matrices | Covariance matrix | Matrix estimation | Graphons | Distance matrix | Matrix completion | Singular value decomposition | NUMBER | graphons | STOCHASTIC BLOCKMODELS | STATISTICS & PROBABILITY | ALGORITHMS | MODEL | latent space model | distance matrix | sochastic blockmodel | covariance matrix | GRAPHS | PREDICTION | low rank matrices | matrix estimation | PENALIZATION | NORM | COMPLETION | singular value decomposition | 62G05 | 05C99 | 60B20 | 62F12

Latent space model | Sochastic blockmodel | Low rank matrices | Covariance matrix | Matrix estimation | Graphons | Distance matrix | Matrix completion | Singular value decomposition | NUMBER | graphons | STOCHASTIC BLOCKMODELS | STATISTICS & PROBABILITY | ALGORITHMS | MODEL | latent space model | distance matrix | sochastic blockmodel | covariance matrix | GRAPHS | PREDICTION | low rank matrices | matrix estimation | PENALIZATION | NORM | COMPLETION | singular value decomposition | 62G05 | 05C99 | 60B20 | 62F12

Journal Article

8.
Full Text
Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices

IEEE Transactions on Signal Processing, ISSN 1053-587X, 01/2015, Volume 63, Issue 1, pp. 81 - 89

For parahermitian polynomial matrices, which can be used, for example, to characterize space-time covariance in broadband array processing, the conventional...

Jacobian matrices | MIMO systems | Correlation | Signal processing algorithms | Polynomials | Broadband communication | Matrix decomposition | parahermitian matrix | Covariance matrices | paraunitary matrix | polynomial matrix eigenvalue decomposition | ENGINEERING, ELECTRICAL & ELECTRONIC | Eigenvalues | Signal processing | Usage | Mathematical optimization | Innovations | Algorithms | Broadband | Transaction processing | Arrays | Polynomial matrices | Convergence

Jacobian matrices | MIMO systems | Correlation | Signal processing algorithms | Polynomials | Broadband communication | Matrix decomposition | parahermitian matrix | Covariance matrices | paraunitary matrix | polynomial matrix eigenvalue decomposition | ENGINEERING, ELECTRICAL & ELECTRONIC | Eigenvalues | Signal processing | Usage | Mathematical optimization | Innovations | Algorithms | Broadband | Transaction processing | Arrays | Polynomial matrices | Convergence

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 9/2012, Volume 25, Issue 3, pp. 655 - 686

Given a probability distribution in ℝ n with general (nonwhite) covariance, a classical estimator of the covariance matrix is the sample covariance matrix...

60H12 | Estimation of covariance matrices | Random matrices with independent columns | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Statistics, general | Sample covariance matrices | 46B09 | STATISTICS & PROBABILITY | CONVEX-BODIES

60H12 | Estimation of covariance matrices | Random matrices with independent columns | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Statistics, general | Sample covariance matrices | 46B09 | STATISTICS & PROBABILITY | CONVEX-BODIES

Journal Article

Journal of the American Statistical Association, ISSN 0162-1459, 06/2011, Volume 106, Issue 494, pp. 672 - 684

In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual...

Support recovery | Spectral norm | Universal thresholding | Optimal rate of convergence | Frobenius norm | Datasets | Statistical variance | Theory and Methods | Threshing | Analytical estimating | Estimation theory | Mathematical vectors | Covariance matrices | Estimators | Consistent estimators | Tumors | STATISTICS & PROBABILITY | WAVELET SHRINKAGE | REGULARIZATION | Research | Analysis of covariance | Mathematical optimization | Analysis | Methods | Threshold (Perception)

Support recovery | Spectral norm | Universal thresholding | Optimal rate of convergence | Frobenius norm | Datasets | Statistical variance | Theory and Methods | Threshing | Analytical estimating | Estimation theory | Mathematical vectors | Covariance matrices | Estimators | Consistent estimators | Tumors | STATISTICS & PROBABILITY | WAVELET SHRINKAGE | REGULARIZATION | Research | Analysis of covariance | Mathematical optimization | Analysis | Methods | Threshold (Perception)

Journal Article

IEEE Transactions on Evolutionary Computation, ISSN 1089-778X, 3/2019, pp. 1 - 1

In this paper, we discuss a method for generating new individuals such that their mean vector and the covariance matrix are defined by formulas analogous to...

Sociology | Differential Evolution | Gaussian distribution | Covariance Matrix Adaptation Evolution Strategy | History | Indexes | Covariance matrices | Optimization | black-box optimization

Sociology | Differential Evolution | Gaussian distribution | Covariance Matrix Adaptation Evolution Strategy | History | Indexes | Covariance matrices | Optimization | black-box optimization

Journal Article

Physics Reports, ISSN 0370-1573, 01/2017, Volume 666, pp. 1 - 109

This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT...

High dimensional statistics | Rotational invariant estimator | Spectral decomposition | Correlation matrix | Random Matrix Theory | SINGULAR-VALUE DECOMPOSITION | PHYSICS, MULTIDISCIPLINARY | LIMITING SPECTRAL DISTRIBUTION | EMPIRICAL DISTRIBUTION | PRINCIPAL COMPONENTS | DISTRIBUTIONS | PORTFOLIO OPTIMIZATION | EIGENVALUES | LARGE DEVIATIONS | COVARIANCE MATRICES | M-ESTIMATOR | Financial markets | Statistical Mechanics | Statistical Finance | Condensed Matter | Statistics | Statistics Theory | Quantitative Finance | Physics

High dimensional statistics | Rotational invariant estimator | Spectral decomposition | Correlation matrix | Random Matrix Theory | SINGULAR-VALUE DECOMPOSITION | PHYSICS, MULTIDISCIPLINARY | LIMITING SPECTRAL DISTRIBUTION | EMPIRICAL DISTRIBUTION | PRINCIPAL COMPONENTS | DISTRIBUTIONS | PORTFOLIO OPTIMIZATION | EIGENVALUES | LARGE DEVIATIONS | COVARIANCE MATRICES | M-ESTIMATOR | Financial markets | Statistical Mechanics | Statistical Finance | Condensed Matter | Statistics | Statistics Theory | Quantitative Finance | Physics

Journal Article

Journal of the Royal Statistical Society. Series B (Statistical Methodology), ISSN 1369-7412, 9/2013, Volume 75, Issue 4, pp. 603 - 680

The paper deals with the estimation of a high dimensional covariance with a conditional sparsity structure and fast diverging eigenvalues. By assuming a sparse...

Covariance | Threshing | Eigenvalues | Principal components analysis | Poetry | Covariance matrices | Financial portfolios | Estimators | Consistent estimators | Estimation methods | Cross‐sectional correlation | Diverging eigenvalues | Thresholding | Sparse matrix | Approximate factor model | Low rank matrix | High dimensionality | Unknown factors | Principal components | Cross-sectional correlation | LARGEST EIGENVALUE | COMPONENTS-ANALYSIS | STATISTICS & PROBABILITY | HIGH-DIMENSION | PORTFOLIO SELECTION | FALSE DISCOVERY | CONSISTENCY | OPTIMAL RATES | DYNAMIC-FACTOR MODEL | MATRIX DECOMPOSITION | LARGE NUMBER | Studies | Mathematical models | Statistical analysis | Matrix | Statistics | Approximation | Asymptotic properties | Complement | Covariance matrix | Convergence | thresholding | diverging eigenvalues | sparse matrix | principal components | approximate factor model | unknown factors | High-dimensionality | cross-sectional correlation | low-rank matrix

Covariance | Threshing | Eigenvalues | Principal components analysis | Poetry | Covariance matrices | Financial portfolios | Estimators | Consistent estimators | Estimation methods | Cross‐sectional correlation | Diverging eigenvalues | Thresholding | Sparse matrix | Approximate factor model | Low rank matrix | High dimensionality | Unknown factors | Principal components | Cross-sectional correlation | LARGEST EIGENVALUE | COMPONENTS-ANALYSIS | STATISTICS & PROBABILITY | HIGH-DIMENSION | PORTFOLIO SELECTION | FALSE DISCOVERY | CONSISTENCY | OPTIMAL RATES | DYNAMIC-FACTOR MODEL | MATRIX DECOMPOSITION | LARGE NUMBER | Studies | Mathematical models | Statistical analysis | Matrix | Statistics | Approximation | Asymptotic properties | Complement | Covariance matrix | Convergence | thresholding | diverging eigenvalues | sparse matrix | principal components | approximate factor model | unknown factors | High-dimensionality | cross-sectional correlation | low-rank matrix

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 07/2011, Volume 33, Issue 7, pp. 1470 - 1481

For many learning problems, estimates of the inverse population covariance are required and often obtained by inverting the sample covariance matrix....

Upper bound | Accuracy | Simulation | linear discriminants | random subspace method | peaking phenomenon | Machine learning | Pseudo-inverse | random matrix theory | Eigenvalues and eigenfunctions | Covariance matrix | Bagging | bagging | SET | HIGH-DIMENSIONAL DATA | LARGEST EIGENVALUE | CLASSIFICATION | TRACE INEQUALITY | COMPONENT ANALYSIS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | DISTRIBUTIONS | ERROR | SELECTION | ASSOCIATION | Measurement | Usage | Specific gravity | Analysis | Eigenvalues | Simulation methods | Methods | Studies | Reconstruction | Errors | Covariance | Mathematical analysis | Data sets | Inverse

Upper bound | Accuracy | Simulation | linear discriminants | random subspace method | peaking phenomenon | Machine learning | Pseudo-inverse | random matrix theory | Eigenvalues and eigenfunctions | Covariance matrix | Bagging | bagging | SET | HIGH-DIMENSIONAL DATA | LARGEST EIGENVALUE | CLASSIFICATION | TRACE INEQUALITY | COMPONENT ANALYSIS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | DISTRIBUTIONS | ERROR | SELECTION | ASSOCIATION | Measurement | Usage | Specific gravity | Analysis | Eigenvalues | Simulation methods | Methods | Studies | Reconstruction | Errors | Covariance | Mathematical analysis | Data sets | Inverse

Journal Article

1970, 337

Book

Journal of the American Statistical Association, ISSN 0162-1459, 09/2012, Volume 107, Issue 499, pp. 1187 - 1200

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with...

Conditional independence | Sparsity | Sparsistency | Penalized likelihood | Matrix-variate normal distribution | Datasets | Maximum likelihood estimation | Penalty function | Gaussian distributions | Covariance | Theory and Methods | Analytical estimating | Matrices | Covariance matrices | Modeling | Estimation methods | REGRESSION | NONCONCAVE PENALIZED LIKELIHOOD | STATISTICS & PROBABILITY | COVARIANCE-MODELS | VARIABLE SELECTION | Analysis | Graph theory

Conditional independence | Sparsity | Sparsistency | Penalized likelihood | Matrix-variate normal distribution | Datasets | Maximum likelihood estimation | Penalty function | Gaussian distributions | Covariance | Theory and Methods | Analytical estimating | Matrices | Covariance matrices | Modeling | Estimation methods | REGRESSION | NONCONCAVE PENALIZED LIKELIHOOD | STATISTICS & PROBABILITY | COVARIANCE-MODELS | VARIABLE SELECTION | Analysis | Graph theory

Journal Article