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2016, Chapman & Hall/CRC handbooks of modern statistical methods, ISBN 9781482249071, xvi, 464 pages

"Handbook of Big Data provides a state-of-the-art overview of the analysis of large-scale datasets. Featuring contributions from well-known experts in...

Big data | Statistical methods | Statistical Theory & Methods | Statistical Computing | Machine Learning | United States

Big data | Statistical methods | Statistical Theory & Methods | Statistical Computing | Machine Learning | United States

Book

2013, 1. Aufl., Selected works in probability and statistics, ISBN 9781461455431, Volume 13, 608

This volume presents selections of Peter J. Bickels major papers, along with comments on their novelty and impact on the subsequent development of statistics as a discipline...

Bickel, Peter J - Criticism and interpretation | Mathematical statistics | Estimation theory

Bickel, Peter J - Criticism and interpretation | Mathematical statistics | Estimation theory

eBook

The Annals of statistics, ISSN 0090-5364, 06/2006, Volume 34, Issue 3, pp. 1436 - 1462

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between...

Maximum likelihood estimation | Gaussian distributions | Neighborhoods | Covariance | Linear regression | Connectivity | Random variables | Covariance matrices | Consistent estimators | Oracles | Graphical Model Methods in Statistics | Gaussian graphical models | Penalized regression | Covariance selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Statistical analysis | Estimating techniques | Regression analysis | 62J07 | covariance selection | 62H20 | 62F12 | penalized regression

Maximum likelihood estimation | Gaussian distributions | Neighborhoods | Covariance | Linear regression | Connectivity | Random variables | Covariance matrices | Consistent estimators | Oracles | Graphical Model Methods in Statistics | Gaussian graphical models | Penalized regression | Covariance selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Statistical analysis | Estimating techniques | Regression analysis | 62J07 | covariance selection | 62H20 | 62F12 | penalized regression

Journal Article

The Annals of statistics, ISSN 0090-5364, 6/2014, Volume 42, Issue 3, pp. 1166 - 1202

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in...

Logistic regression | Generalized linear model | Linear regression | Eigenvalues | Inference | Non Gaussianity | Linear models | Estimators | Consistent estimators | Confidence interval | Central limit theorem | Sparsity | Lasso | Semiparametric efficiency | Multiple testing | Linear model | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Confidence intervals | Mathematical models | Normal distribution | Asymptotic methods | Generalized linear models | generalized linear model | lasso | 62J07 | multiple testing | semiparametric efficiency | linear model | sparsity | 62F25 | 62J12

Logistic regression | Generalized linear model | Linear regression | Eigenvalues | Inference | Non Gaussianity | Linear models | Estimators | Consistent estimators | Confidence interval | Central limit theorem | Sparsity | Lasso | Semiparametric efficiency | Multiple testing | Linear model | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Confidence intervals | Mathematical models | Normal distribution | Asymptotic methods | Generalized linear models | generalized linear model | lasso | 62J07 | multiple testing | semiparametric efficiency | linear model | sparsity | 62F25 | 62J12

Journal Article

The Annals of statistics, ISSN 0090-5364, 4/2006, Volume 34, Issue 2, pp. 559 - 583

We prove that boosting with the squared error loss, L₂Boosting, is consistent for very high-dimensional linear models, where the number of predictor variables...

Regression coefficients | Componentwise operations | Sample size | Linear regression | Least squares | Mathematical functions | Boosting and Thresholding | Gene expression | Linear models | Modeling | Oracles | Overcomplete dictionary | Sparsity | Lasso | Matching pursuit | Weak greedy algorithm | Binary classification | Variable selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Linear programming | Mathematical models | Algorithms | Statistical analysis | Classification | 62J05 | 62P10 | 62J07 | sparsity | matching pursuit | overcomplete dictionary | variable selection | 49M15 | weak greedy algorithm | 68Q32 | gene expression

Regression coefficients | Componentwise operations | Sample size | Linear regression | Least squares | Mathematical functions | Boosting and Thresholding | Gene expression | Linear models | Modeling | Oracles | Overcomplete dictionary | Sparsity | Lasso | Matching pursuit | Weak greedy algorithm | Binary classification | Variable selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Linear programming | Mathematical models | Algorithms | Statistical analysis | Classification | 62J05 | 62P10 | 62J07 | sparsity | matching pursuit | overcomplete dictionary | variable selection | 49M15 | weak greedy algorithm | 68Q32 | gene expression

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2014, Volume 42, Issue 6, pp. 2526 - 2556

We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among...

Additivity | Maximum likelihood estimation | Error rates | Identifiability | Directed acyclic graphs | Machine learning | Maximum likelihood estimators | Structural equation models | Consistent estimators | Estimation methods | Graphical modeling | Intervention calculus | Sparsity | Structural equation model | Nonparametric regression | Regularized estimation | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Decision making models | Probability distribution | Regression analysis | Estimating techniques | Causality | Maximum likelihood method | nonparametric regression | 68T99 | regularized estimation | sparsity | 62G99 | intervention calculus | 62H99 | structural equation model

Additivity | Maximum likelihood estimation | Error rates | Identifiability | Directed acyclic graphs | Machine learning | Maximum likelihood estimators | Structural equation models | Consistent estimators | Estimation methods | Graphical modeling | Intervention calculus | Sparsity | Structural equation model | Nonparametric regression | Regularized estimation | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Decision making models | Probability distribution | Regression analysis | Estimating techniques | Causality | Maximum likelihood method | nonparametric regression | 68T99 | regularized estimation | sparsity | 62G99 | intervention calculus | 62H99 | structural equation model

Journal Article

The Annals of statistics, ISSN 0090-5364, 8/2015, Volume 43, Issue 4, pp. 1801 - 1830

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources....

Aggregation | Big data | Robustness | Regularization | Mixture models | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical problems | Theoretical mathematics | Mathematical models | Regression analysis | Estimating techniques | Random variables | Statistics - Methodology | robustness | aggregation | big data | 62J07 | regularization

Aggregation | Big data | Robustness | Regularization | Mixture models | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical problems | Theoretical mathematics | Mathematical models | Regression analysis | Estimating techniques | Random variables | Statistics - Methodology | robustness | aggregation | big data | 62J07 | regularization

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2009, Volume 37, Issue 6B, pp. 3779 - 3821

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for...

Supernova remnants | Generalized linear model | Mathematical constants | Mathematical functions | Standard deviation | Random variables | Data smoothing | Modeling | Estimators | Oracles | Oracle inequality | Sparsity | Group lasso | Model selection | Penalized likelihood | Nonparametric regression | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Models | Estimating techniques | Mathematical analysis | Statistics - Machine Learning | nonparametric regression | penalized likelihood | 62G08 | 62J07 | oracle inequality | model selection | sparsity | 62F12

Supernova remnants | Generalized linear model | Mathematical constants | Mathematical functions | Standard deviation | Random variables | Data smoothing | Modeling | Estimators | Oracles | Oracle inequality | Sparsity | Group lasso | Model selection | Penalized likelihood | Nonparametric regression | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Models | Estimating techniques | Mathematical analysis | Statistics - Machine Learning | nonparametric regression | penalized likelihood | 62G08 | 62J07 | oracle inequality | model selection | sparsity | 62F12

Journal Article

The Annals of statistics, ISSN 0090-5364, 4/2013, Volume 41, Issue 2, pp. 436 - 463

Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of...

Gaussian distributions | Algebra | Directed acyclic graphs | Surface areas | Hypersurfaces | Hyperplanes | Inference | Polynomials | Skeleton | Vertices | Causal inference | Directed acyclic graph | (strong) faithfulness | Conditional independence | Real algebraic hypersurface | Structural equation model | Crofton's formula | Algebraic statistics | PC-algorithm | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Geometry | Studies | Normal distribution | Correlation analysis | Measurement techniques | Graph algorithms | Causality | conditional independence | 62H05 | algebraic statistics | real algebraic hypersurface | Crofton’s formula | 14Q10 | directed acyclic graph | 62H20 | structural equation model

Gaussian distributions | Algebra | Directed acyclic graphs | Surface areas | Hypersurfaces | Hyperplanes | Inference | Polynomials | Skeleton | Vertices | Causal inference | Directed acyclic graph | (strong) faithfulness | Conditional independence | Real algebraic hypersurface | Structural equation model | Crofton's formula | Algebraic statistics | PC-algorithm | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Geometry | Studies | Normal distribution | Correlation analysis | Measurement techniques | Graph algorithms | Causality | conditional independence | 62H05 | algebraic statistics | real algebraic hypersurface | Crofton’s formula | 14Q10 | directed acyclic graph | 62H20 | structural equation model

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2009, Volume 37, Issue 6A, pp. 3133 - 3164

We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from...

Equivalence relation | Datasets | Sample size | Multisets | Directed acyclic graphs | Inference | Consistent estimators | Vertices | Estimation methods | Absolute value | Graphical modeling | Intervention calculus | Causal analysis | Sparsity | PC-algorithm | Directed acyclic graph (DAG) | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Calculus | Algorithms | Causality | Graph representations | Statistics - Methodology | directed acyclic graph (DAG) | graphical modeling | sparsity | 62-09 | intervention calculus | 62H99

Equivalence relation | Datasets | Sample size | Multisets | Directed acyclic graphs | Inference | Consistent estimators | Vertices | Estimation methods | Absolute value | Graphical modeling | Intervention calculus | Causal analysis | Sparsity | PC-algorithm | Directed acyclic graph (DAG) | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Calculus | Algorithms | Causality | Graph representations | Statistics - Methodology | directed acyclic graph (DAG) | graphical modeling | sparsity | 62-09 | intervention calculus | 62H99

Journal Article

Journal of the Royal Statistical Society. Series B, Statistical methodology, ISSN 1369-7412, 07/2010, Volume 72, Issue 4, pp. 417 - 473

Estimation of structure, such as in variable selection, graphical modelling or cluster analysis, is notoriously difficult, especially for high dimensional...

Datasets | Regression coefficients | False positive errors | Linear regression | Machine learning | Eigenvalues | Mathematical independent variables | Gene expression | Modeling | Linear models | Structure estimation | Stability selection | High dimensional data | Resampling | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Analysis | Algorithms | Statistical data | Studies | Cluster analysis | Estimating techniques | Research methodology | Sampling techniques | Stability | Mathematical analysis | Samples | Consistency | Gaussian | Mathematical models | Modelling | Models

Datasets | Regression coefficients | False positive errors | Linear regression | Machine learning | Eigenvalues | Mathematical independent variables | Gene expression | Modeling | Linear models | Structure estimation | Stability selection | High dimensional data | Resampling | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Analysis | Algorithms | Statistical data | Studies | Cluster analysis | Estimating techniques | Research methodology | Sampling techniques | Stability | Mathematical analysis | Samples | Consistency | Gaussian | Mathematical models | Modelling | Models

Journal Article

Clinical cancer research, ISSN 1557-3265, 12/2009, Volume 16, Issue 1, pp. 88 - 98

Purpose: Tumor stage and nuclear grade are the most important prognostic parameters of clear cell renal cell carcinoma (ccRCC). The
progression risk of ccRCC...

Life Sciences & Biomedicine | Oncology | Science & Technology | Prognosis | Biomarkers, Tumor - analysis | Carcinoma, Renal Cell - pathology | Humans | Middle Aged | Linear Models | Male | Kidney Neoplasms - metabolism | Kidney Neoplasms - mortality | Disease Progression | Carcinoma, Renal Cell - metabolism | Carcinoma, Renal Cell - mortality | Phenotype | Adolescent | Aged, 80 and over | Protein Array Analysis | Adult | Female | Kidney Neoplasms - pathology | Neoplasm Proteins - analysis | Aged | Neoplasm Staging | Index Medicus

Life Sciences & Biomedicine | Oncology | Science & Technology | Prognosis | Biomarkers, Tumor - analysis | Carcinoma, Renal Cell - pathology | Humans | Middle Aged | Linear Models | Male | Kidney Neoplasms - metabolism | Kidney Neoplasms - mortality | Disease Progression | Carcinoma, Renal Cell - metabolism | Carcinoma, Renal Cell - mortality | Phenotype | Adolescent | Aged, 80 and over | Protein Array Analysis | Adult | Female | Kidney Neoplasms - pathology | Neoplasm Proteins - analysis | Aged | Neoplasm Staging | Index Medicus

Journal Article

The Annals of statistics, ISSN 0090-5364, 8/2002, Volume 30, Issue 4, pp. 927 - 961

Bagging is one of the most effective computationally intensive procedures to improve on unstable estimators or classifiers, useful especially for high...

Aggregation | Brownian motion | Statistical variance | Nonparametric Classification | Sample size | Linear regression | Decision trees | Data smoothing | Modeling | Tree stumps | Estimators | Model selection | MARS | Classification | Multiple predictions | Nonparametric regression | Bootstrap | Decision tree | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | nonparametric regression | decision tree | 68T10 | 62G08 | 62G09 | model selection | 62H30 | multiple predictions | classification

Aggregation | Brownian motion | Statistical variance | Nonparametric Classification | Sample size | Linear regression | Decision trees | Data smoothing | Modeling | Tree stumps | Estimators | Model selection | MARS | Classification | Multiple predictions | Nonparametric regression | Bootstrap | Decision tree | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | nonparametric regression | decision tree | 68T10 | 62G08 | 62G09 | model selection | 62H30 | multiple predictions | classification

Journal Article

Computational statistics, ISSN 1613-9658, 07/2013, Volume 29, Issue 3-4, pp. 407 - 430

..., with an empirical comparison
Peter Bühlmann · Jacopo Mandozzi
Received: 3 September 2012 / Accepted: 1 July 2013 / Published online: 23 July 2013
© Springer-Verlag Berlin...

Sparsity | Sure independence screening | Lasso | Probability Theory and Stochastic Processes | Economic Theory | Elastic net | Statistics, general | Statistics | Linear model | Probability and Statistics in Computer Science | Ridge | Variable selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Statistical methods | Regression analysis | Generalized linear models | Regression coefficients | Screening | Least squares method | Mathematical analysis | Bias | Mathematical models | Empirical analysis

Sparsity | Sure independence screening | Lasso | Probability Theory and Stochastic Processes | Economic Theory | Elastic net | Statistics, general | Statistics | Linear model | Probability and Statistics in Computer Science | Ridge | Variable selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Statistical methods | Regression analysis | Generalized linear models | Regression coefficients | Screening | Least squares method | Mathematical analysis | Bias | Mathematical models | Empirical analysis

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2011, Volume 39, Issue 6, pp. 3369 - 3391

Test statistics are often strongly dependent in large-scale multiple testing applications. Most corrections for multiplicity are unduly conservative for...

Mathematical procedures | Null hypothesis | Determinism | Permutation tests | Sample size | Applied statistics | P values | Random variables | Statistics | Oracles | Permutations | Sparsity | Multiple testing under dependence | Rank-based nonparametric tests | Asymptotic optimality | Westfall-Young procedure | High-dimensional inference | Familywise error rate | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Statistical methods | Asymptotic methods | Dependence | Testing | high-dimensional inference | 62J15 | asymptotic optimality | sparsity | permutations | familywise error rate | rank-based nonparametric tests | 62F03 | Westfall–Young procedure

Mathematical procedures | Null hypothesis | Determinism | Permutation tests | Sample size | Applied statistics | P values | Random variables | Statistics | Oracles | Permutations | Sparsity | Multiple testing under dependence | Rank-based nonparametric tests | Asymptotic optimality | Westfall-Young procedure | High-dimensional inference | Familywise error rate | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Statistical methods | Asymptotic methods | Dependence | Testing | high-dimensional inference | 62J15 | asymptotic optimality | sparsity | permutations | familywise error rate | rank-based nonparametric tests | 62F03 | Westfall–Young procedure

Journal Article