The Annals of Statistics, ISSN 0090-5364, 4/2012, Volume 40, Issue 2, pp. 1171 - 1197

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations...

Factor analysis | Covariance | Error bounds | Principal components analysis | Matrices | Mathematical vectors | Convexity | Covariance matrices | Modeling | Estimators | High-dimensional inference | Composite regularizers | Nuclear norm | LINEAR-REGRESSION | composite regularizers | STATISTICS & PROBABILITY | LOW-RANK MATRICES | nuclear norm | 62H12 | 62F30

Factor analysis | Covariance | Error bounds | Principal components analysis | Matrices | Mathematical vectors | Convexity | Covariance matrices | Modeling | Estimators | High-dimensional inference | Composite regularizers | Nuclear norm | LINEAR-REGRESSION | composite regularizers | STATISTICS & PROBABILITY | LOW-RANK MATRICES | nuclear norm | 62H12 | 62F30

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2011, Volume 39, Issue 2, pp. 1069 - 1097

We study an instance of high-dimensional inference in which the goal is to estimate a matrix Θ* ∈ ℝ m₁ × m₂ on the basis of N noisy observations. The unknown...

Error rates | Technical reports | Sample size | Autoregressive models | Linear regression | Error bounds | Matrices | Mathematical vectors | System identification | Covariance matrices | REGRESSION | nuclear norm | APPROXIMATION | STATISTICS & PROBABILITY | MODEL | NORM MINIMIZATION | VARIABLE SELECTION | PRINCIPAL COMPONENTS | M-estimators | RECOVERY | LASSO | random matrix theory | rank constraints | High-dimensional inference | trace norm | REGULARIZATION | COVARIANCE ESTIMATION | 62F30 | 62H12

Error rates | Technical reports | Sample size | Autoregressive models | Linear regression | Error bounds | Matrices | Mathematical vectors | System identification | Covariance matrices | REGRESSION | nuclear norm | APPROXIMATION | STATISTICS & PROBABILITY | MODEL | NORM MINIMIZATION | VARIABLE SELECTION | PRINCIPAL COMPONENTS | M-estimators | RECOVERY | LASSO | random matrix theory | rank constraints | High-dimensional inference | trace norm | REGULARIZATION | COVARIANCE ESTIMATION | 62F30 | 62H12

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 2019, pp. 1 - 15

Journal Article

Annals of Statistics, ISSN 0090-5364, 02/2016, Volume 44, Issue 1, pp. 87 - 112

The beta-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key...

Differential privacy | Existence of MLE | Degree sequence | β-model | Measurement error | measurement error | NUMBER | beta-model | existence of MLE | STATISTICS & PROBABILITY | VERTICES | SOCIAL NETWORKS | differential privacy | 91D30 | 62F30 | 62F12

Differential privacy | Existence of MLE | Degree sequence | β-model | Measurement error | measurement error | NUMBER | beta-model | existence of MLE | STATISTICS & PROBABILITY | VERTICES | SOCIAL NETWORKS | differential privacy | 91D30 | 62F30 | 62F12

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2014, Volume 42, Issue 6, pp. 2164 - 2201

We provide theoretical analysis of the statistical and computational properties of penalized M-estimators that can be formulated as the solution to a possibly...

Objective functions | Statistical properties | Statistical theories | Least squares | Learning disabilities | Estimators | Perceptron convergence procedure | Logistics | Oracles | Computational statistics | Optimal statistical rate | Nonconvex regularized M-estimation | Geometric computational rate | Path-following method | REGRESSION | PATH | GRADIENT METHODS | geometric computational rate | ALGORITHM | STATISTICS & PROBABILITY | MULTISTAGE CONVEX RELAXATION | GENERALIZED LINEAR-MODELS | VARIABLE SELECTION | NONCONCAVE PENALIZED LIKELIHOOD | path-following method | optimal statistical rate | LASSO | REGULARIZATION | Statistics - Machine Learning | 90C52 | 62F30 | 90C26 | 62J12

Objective functions | Statistical properties | Statistical theories | Least squares | Learning disabilities | Estimators | Perceptron convergence procedure | Logistics | Oracles | Computational statistics | Optimal statistical rate | Nonconvex regularized M-estimation | Geometric computational rate | Path-following method | REGRESSION | PATH | GRADIENT METHODS | geometric computational rate | ALGORITHM | STATISTICS & PROBABILITY | MULTISTAGE CONVEX RELAXATION | GENERALIZED LINEAR-MODELS | VARIABLE SELECTION | NONCONCAVE PENALIZED LIKELIHOOD | path-following method | optimal statistical rate | LASSO | REGULARIZATION | Statistics - Machine Learning | 90C52 | 62F30 | 90C26 | 62J12

Journal Article

The Annals of Statistics, ISSN 0090-5364, 10/2012, Volume 40, Issue 5, pp. 2452 - 2482

Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based...

Algorithms | Sample size | Linear regression | Statistical theories | Errors in statistics | Matrices | Mathematical vectors | Convexity | Estimators | Perceptron convergence procedure | High-dimensional inference | Convex optimization | Regularized Mestimation | SPARSITY | LINEAR-REGRESSION | DECOMPOSITION | STATISTICS & PROBABILITY | LOW-RANK MATRICES | VARIABLE SELECTION | PURSUIT | SHRINKAGE | LASSO | regularized M-estimation | convex optimization | COMPLETION | NOISY | 62H12 | 62F30

Algorithms | Sample size | Linear regression | Statistical theories | Errors in statistics | Matrices | Mathematical vectors | Convexity | Estimators | Perceptron convergence procedure | High-dimensional inference | Convex optimization | Regularized Mestimation | SPARSITY | LINEAR-REGRESSION | DECOMPOSITION | STATISTICS & PROBABILITY | LOW-RANK MATRICES | VARIABLE SELECTION | PURSUIT | SHRINKAGE | LASSO | regularized M-estimation | convex optimization | COMPLETION | NOISY | 62H12 | 62F30

Journal Article

7.
Full Text
A general testing for order restriction on mean vectors of multivariate normal populations

Communications in Statistics: Simulation and Computation, ISSN 0361-0918, 2018, pp. 1 - 17

Journal Article

Annals of Statistics, ISSN 0090-5364, 12/2017, Volume 45, Issue 6, pp. 2565 - 2589

We propose L-p distance-based goodness-of-fit (GOF) tests for uniform stochastic ordering with two continuous distributions F and G, both of which are unknown....

Order-restricted inference | Star-shaped ordering | Ordinal dominance curve | Hazard rate ordering | Least favorable distribution | Brownian bridge | order-restricted inference | STATISTICS & PROBABILITY | INFERENCE | CONSTRAINT | SURVIVAL FUNCTIONS | DISTRIBUTIONS | hazard rate ordering | ordinal dominance curve | CURVE | least favorable distribution | star-shaped ordering | LIKELIHOOD | secondary 62F30 | Primary 62G10

Order-restricted inference | Star-shaped ordering | Ordinal dominance curve | Hazard rate ordering | Least favorable distribution | Brownian bridge | order-restricted inference | STATISTICS & PROBABILITY | INFERENCE | CONSTRAINT | SURVIVAL FUNCTIONS | DISTRIBUTIONS | hazard rate ordering | ordinal dominance curve | CURVE | least favorable distribution | star-shaped ordering | LIKELIHOOD | secondary 62F30 | Primary 62G10

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 04/2016, Volume 77, Issue 2, pp. 251 - 263

We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong...

numerical range | 54C10 | 82B26 | strong continuity | strong stability | continuity | 47A12 | maximum-entropy inference | Primary 81P16 | 62F30 | 94A17 | Secondary 47N50 | stability | Strong continuity | Strong stability | Numerical range | Continuity | Maximum-entropy inference | Stability | CONVEX-SETS | PHYSICS, MATHEMATICAL | GEOMETRY | Discontinuity | Equivalence | Mathematical analysis | Eigenvalues | Inference | Mathematical models | Inverse | Continuity (mathematics)

numerical range | 54C10 | 82B26 | strong continuity | strong stability | continuity | 47A12 | maximum-entropy inference | Primary 81P16 | 62F30 | 94A17 | Secondary 47N50 | stability | Strong continuity | Strong stability | Numerical range | Continuity | Maximum-entropy inference | Stability | CONVEX-SETS | PHYSICS, MATHEMATICAL | GEOMETRY | Discontinuity | Equivalence | Mathematical analysis | Eigenvalues | Inference | Mathematical models | Inverse | Continuity (mathematics)

Journal Article

Entropy, ISSN 1099-4300, 06/2019, Volume 21, Issue 6, p. 596

In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard...

Maximum likelihood | Data separation | Maximum entropy | Binary regression | Score function | score function | PHYSICS, MULTIDISCIPLINARY | maximum likelihood | 62F30 | 62P25 | RECOVERING INFORMATION | maximum entropy | binary regression | data separation | 62J12 | Statistics - Computation

Maximum likelihood | Data separation | Maximum entropy | Binary regression | Score function | score function | PHYSICS, MULTIDISCIPLINARY | maximum likelihood | 62F30 | 62P25 | RECOVERING INFORMATION | maximum entropy | binary regression | data separation | 62J12 | Statistics - Computation

Journal Article

Journal of Multivariate Analysis, ISSN 0047-259X, 2009, Volume 100, Issue 1, pp. 16 - 36

We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual...

62F30 | 62F10 | Duality | Maximum likelihood | Parametric estimation | Boundary valued parameter | 62F03 | Power function | Parametric test | Mixture | [formula omitted]-divergence | φ{symbol}-divergence | ROBUSTNESS | STATISTICS | phi-divergence | STATISTICS & PROBABILITY | MINIMUM HELLINGER DISTANCE | MULTINOMIAL GOODNESS | DISTRIBUTIONS | FIT | MODELS | PHI-DIVERGENCES | EFFICIENCY | LIKELIHOOD | 62F03 62F10 62F30 Parametric estimation Parametric test Maximum likelihood Mixture Boundary valued parameter Power function Duality [phi]-divergence | Statistics | Mathematics

62F30 | 62F10 | Duality | Maximum likelihood | Parametric estimation | Boundary valued parameter | 62F03 | Power function | Parametric test | Mixture | [formula omitted]-divergence | φ{symbol}-divergence | ROBUSTNESS | STATISTICS | phi-divergence | STATISTICS & PROBABILITY | MINIMUM HELLINGER DISTANCE | MULTINOMIAL GOODNESS | DISTRIBUTIONS | FIT | MODELS | PHI-DIVERGENCES | EFFICIENCY | LIKELIHOOD | 62F03 62F10 62F30 Parametric estimation Parametric test Maximum likelihood Mixture Boundary valued parameter Power function Duality [phi]-divergence | Statistics | Mathematics

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2014, Volume 42, Issue 6, pp. 2340 - 2381

Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution...

Minimax | Maximum likelihood estimation | Line segments | Least squares | Mathematical constants | Mathematical functions | Mathematical inequalities | Random variables | Preprints | Estimators | isotonic regression | DANTZIG SELECTOR | lasso | empirical process | STATISTICS & PROBABILITY | denoising | SPARSITY ORACLE INEQUALITIES | convex constraint | CONSISTENCY | RECOVERY | ESTIMATORS | maximum likelihood | FREEDOM | REGRESSION SHRINKAGE | WAVELET SHRINKAGE | 62G08 | 62F30 | 62F10 | 62F12

Minimax | Maximum likelihood estimation | Line segments | Least squares | Mathematical constants | Mathematical functions | Mathematical inequalities | Random variables | Preprints | Estimators | isotonic regression | DANTZIG SELECTOR | lasso | empirical process | STATISTICS & PROBABILITY | denoising | SPARSITY ORACLE INEQUALITIES | convex constraint | CONSISTENCY | RECOVERY | ESTIMATORS | maximum likelihood | FREEDOM | REGRESSION SHRINKAGE | WAVELET SHRINKAGE | 62G08 | 62F30 | 62F10 | 62F12

Journal Article

Communications in Statistics - Simulation and Computation, ISSN 0361-0918, 08/2018, Volume 47, Issue 7, pp. 1890 - 1898

Many procedures exist for testing equality of means or medians to compare several independent distributions. However, the mean or median do not determine the...

Quantiles | 62F03 | Likelihood ratio test | Actual size | 62F30 | Generalized p-value | PERCENTILES | LOG-NORMAL DISTRIBUTIONS | RATIO | STATISTICS & PROBABILITY | SAMPLE INFERENCE | Likelihood ratio | Equality | Computer simulation | Test procedures

Quantiles | 62F03 | Likelihood ratio test | Actual size | 62F30 | Generalized p-value | PERCENTILES | LOG-NORMAL DISTRIBUTIONS | RATIO | STATISTICS & PROBABILITY | SAMPLE INFERENCE | Likelihood ratio | Equality | Computer simulation | Test procedures

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2019, Volume 174, Issue 1, pp. 77 - 97

In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of...

Semidefinite programming | Theoretical, Mathematical and Computational Physics | Nondegeneracy | Mathematics | Matrix completion problem | Asymptotics | Minimum trace factor analysis | Mathematical Methods in Physics | Minimum rank | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C22 | 62F30 | Statistical inference | 62F12 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Perturbation theory | Factor analysis | Perturbation methods | Covariance | Covariance matrix | Mathematical programming

Semidefinite programming | Theoretical, Mathematical and Computational Physics | Nondegeneracy | Mathematics | Matrix completion problem | Asymptotics | Minimum trace factor analysis | Mathematical Methods in Physics | Minimum rank | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C22 | 62F30 | Statistical inference | 62F12 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Perturbation theory | Factor analysis | Perturbation methods | Covariance | Covariance matrix | Mathematical programming

Journal Article

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Full Text
Successive comparisons between ordered normal means using isotonic regression estimators

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 04/2017, Volume 46, Issue 7, pp. 3186 - 3199

In this study we discuss multiple comparison procedures for checking differences among a sequence of normal means with ordered restriction. Lee and Spurrier (...

62H15 | Likelihood ratio test estimator | Multivariate t-distribution | Power comparison | 62F30 | Statistical analysis | Samples | Constrictions | Regression | Statistical methods | Statistics | Estimators

62H15 | Likelihood ratio test estimator | Multivariate t-distribution | Power comparison | 62F30 | Statistical analysis | Samples | Constrictions | Regression | Statistical methods | Statistics | Estimators

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2006, Volume 34, Issue 6, pp. 2790 - 2824

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing...

Maximum likelihood estimation | Density estimation | Time series models | Approximation | Semiparametric and Nonparametric Inference | Stationary processes | Spectral energy distribution | Time series | Entropy | Mathematical functions | Estimators | Empirical spectral process | Sieve estimation | Exponential inequalities for quadratic forms | Nonparametric maximum likelihood estimation | Locally stationary processes | exponential inequalities for quadratic forms | locally stationary processes | RATES | nonparametric maximum likelihood estimation | MODELS | empirical spectral process | TIME-SERIES | MINIMUM CONTRAST ESTIMATORS | CONVERGENCE | STATISTICS & PROBABILITY | sieve estimation | 62M10 | 62F30

Maximum likelihood estimation | Density estimation | Time series models | Approximation | Semiparametric and Nonparametric Inference | Stationary processes | Spectral energy distribution | Time series | Entropy | Mathematical functions | Estimators | Empirical spectral process | Sieve estimation | Exponential inequalities for quadratic forms | Nonparametric maximum likelihood estimation | Locally stationary processes | exponential inequalities for quadratic forms | locally stationary processes | RATES | nonparametric maximum likelihood estimation | MODELS | empirical spectral process | TIME-SERIES | MINIMUM CONTRAST ESTIMATORS | CONVERGENCE | STATISTICS & PROBABILITY | sieve estimation | 62M10 | 62F30

Journal Article

The Annals of Statistics, ISSN 0090-5364, 04/2013, Volume 41, Issue 2, pp. 536 - 567

We consider the problem of regularized maximum likelihood estimation for the structure and parameters of a high-dimensional, sparse directed acyclic graphical...

Causal inference | faithfulness condition | high-dimensional inference | graphical modeling | 62F30 | 62F12 | Gaussian structural equation model

Causal inference | faithfulness condition | high-dimensional inference | graphical modeling | 62F30 | 62F12 | Gaussian structural equation model

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 06/2019, Volume 48, Issue 11, pp. 2748 - 2765

Improved point and interval estimation of the smallest scale parameter of n independent populations following two-parameter exponential distributions are...

Maruyama-type estimators | Stein-type estimators | Decision theory | 62C99 | 62F30 | 62F99 | Strawderman-type estimators | Kubokawa's methodology | Brewster and Zidek-type estimators | Kubokawa’s methodology | STATISTICS & PROBABILITY | INADMISSIBILITY | VARIANCE | Sampling | Parameter estimation | Estimators

Maruyama-type estimators | Stein-type estimators | Decision theory | 62C99 | 62F30 | 62F99 | Strawderman-type estimators | Kubokawa's methodology | Brewster and Zidek-type estimators | Kubokawa’s methodology | STATISTICS & PROBABILITY | INADMISSIBILITY | VARIANCE | Sampling | Parameter estimation | Estimators

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2014, Volume 42, Issue 2, pp. 532 - 562

Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and...

Gaussian distributions | Covariance | Correlations | Machine learning | Kronecker product | Matrices | Covariance matrices | Estimators | Estimation methods | Perceptron convergence procedure | Graphical Lasso | Inverse covariance estimation | Graphical model selection | Covariance estimation | Matrix variate normal distribution | inverse covariance estimation | covariance estimation | NONCONCAVE PENALIZED LIKELIHOOD | DIMENSIONAL COVARIANCE ESTIMATION | MODELS | matrix variate normal distribution | LASSO | CONVERGENCE | STATISTICS & PROBABILITY | SELECTION | graphical Lasso | 62F30 | 62F12

Gaussian distributions | Covariance | Correlations | Machine learning | Kronecker product | Matrices | Covariance matrices | Estimators | Estimation methods | Perceptron convergence procedure | Graphical Lasso | Inverse covariance estimation | Graphical model selection | Covariance estimation | Matrix variate normal distribution | inverse covariance estimation | covariance estimation | NONCONCAVE PENALIZED LIKELIHOOD | DIMENSIONAL COVARIANCE ESTIMATION | MODELS | matrix variate normal distribution | LASSO | CONVERGENCE | STATISTICS & PROBABILITY | SELECTION | graphical Lasso | 62F30 | 62F12

Journal Article

Journal of Applied Statistics, ISSN 0266-4763, 07/2017, Volume 44, Issue 10, pp. 1743 - 1760

A medical examination provides a key input into decisions about disability pension and other forms of income support or compensation that are justified on...

Assessment | Fisher scoring algorithm | 62F30 | 62F10 | disability score | score inflation | discrete linear distribution | STATISTICS & PROBABILITY | Disabilities | Sensitivity analysis | Assessments | Disability pensions

Assessment | Fisher scoring algorithm | 62F30 | 62F10 | disability score | score inflation | discrete linear distribution | STATISTICS & PROBABILITY | Disabilities | Sensitivity analysis | Assessments | Disability pensions

Journal Article

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