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## Search Articles

The Annals of statistics, ISSN 0090-5364, 04/2010, Volume 38, Issue 2, pp. 635 - 669

A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for...

Quantile regression | Halfspace depth | Multivariate quantile | Studies | Linear programming | Multivariate analysis | Optimization | quantile regression | 62H05 | halfspace depth | 62J05

Quantile regression | Halfspace depth | Multivariate quantile | Studies | Linear programming | Multivariate analysis | Optimization | quantile regression | 62H05 | halfspace depth | 62J05

Journal Article

The Annals of statistics, ISSN 0090-5364, 8/2009, Volume 37, Issue 4, pp. 1591 - 1646

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set g up to the...

Aggregation | Statistical variance | Minimax | Probability distributions | Learning rate | Least squares | Mathematical functions | Learning theory | Random variables | Estimators | Statistical learning | Lower bounds in VC-classes | Convex loss | Excess risk | Minimax lower bounds | Lq -regression | Fast rates of convergence | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Probability | Rates | Algorithms | Predictions | convex loss | 62H05 | minimax lower bounds | 68T10 | 62G08 | fast rates of convergence | aggregation | lower bounds in VC-classes | L_q-regression | excess risk

Aggregation | Statistical variance | Minimax | Probability distributions | Learning rate | Least squares | Mathematical functions | Learning theory | Random variables | Estimators | Statistical learning | Lower bounds in VC-classes | Convex loss | Excess risk | Minimax lower bounds | Lq -regression | Fast rates of convergence | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Probability | Rates | Algorithms | Predictions | convex loss | 62H05 | minimax lower bounds | 68T10 | 62G08 | fast rates of convergence | aggregation | lower bounds in VC-classes | L_q-regression | excess risk

Journal Article

The Annals of statistics, ISSN 0090-5364, 08/2005, Volume 33, Issue 4, pp. 1580 - 1616

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These...

Ellipticity | Dimensionality reduction | Model Selection and Dimension Reduction | Statistical variance | Sufficient conditions | Linear regression | Eigenvalues | Eigenvectors | Matrices | Estimators | Estimation methods | Central subspace | Data visualization | Empirical directions | Nonparametric regression | PCA | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Visualization | Regression analysis | Simulation | nonparametric regression | 62H05 | 62G08 | 62G09 | empirical directions | data visualization

Ellipticity | Dimensionality reduction | Model Selection and Dimension Reduction | Statistical variance | Sufficient conditions | Linear regression | Eigenvalues | Eigenvectors | Matrices | Estimators | Estimation methods | Central subspace | Data visualization | Empirical directions | Nonparametric regression | PCA | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Visualization | Regression analysis | Simulation | nonparametric regression | 62H05 | 62G08 | 62G09 | empirical directions | data visualization

Journal Article

The Annals of statistics, ISSN 0090-5364, 4/2007, Volume 35, Issue 2, pp. 608 - 633

It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes...

Integers | Minimax | Statistical Learning Theory | Probability distributions | Learning rate | Lebesgue measures | Mathematical functions | Polynomials | Density | Estimators | Perceptron convergence procedure | Excess risk | Statistical learning | Minimax lower bounds | Classification | Plug-in classifiers | Fast rates of convergence | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Bayesian analysis | Convergence | Probability | 62H05 | statistical learning | minimax lower bounds | 62G07 | 68T10 | 62G08 | fast rates of convergence | plug-in classifiers | excess risk

Integers | Minimax | Statistical Learning Theory | Probability distributions | Learning rate | Lebesgue measures | Mathematical functions | Polynomials | Density | Estimators | Perceptron convergence procedure | Excess risk | Statistical learning | Minimax lower bounds | Classification | Plug-in classifiers | Fast rates of convergence | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Bayesian analysis | Convergence | Probability | 62H05 | statistical learning | minimax lower bounds | 62G07 | 68T10 | 62G08 | fast rates of convergence | plug-in classifiers | excess risk

Journal Article

The Annals of statistics, ISSN 0090-5364, 10/2005, Volume 33, Issue 5, pp. 2042 - 2065

Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features...

Mathematical manifolds | Local maximum | Critical points | Mixture Models | Mathematical functions | Mathematical vectors | Surface contours | Ellipses | Curvature | Topographical elevation | Contour lines | Dimension reduction | Manifold | Topography | Multivariate mode | Clustering | Mixture | Modal cluster | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Cluster analysis | Mathematical models | Multivariate analysis | Statistics | 62H05 | topography | 62E10 | manifold | 62H30 | clustering | multivariate mode | dimension reduction | modal cluster

Mathematical manifolds | Local maximum | Critical points | Mixture Models | Mathematical functions | Mathematical vectors | Surface contours | Ellipses | Curvature | Topographical elevation | Contour lines | Dimension reduction | Manifold | Topography | Multivariate mode | Clustering | Mixture | Modal cluster | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Cluster analysis | Mathematical models | Multivariate analysis | Statistics | 62H05 | topography | 62E10 | manifold | 62H30 | clustering | multivariate mode | dimension reduction | modal cluster

Journal Article

02/2017

Gaussian mixture models are widely used in Statistics. A fundamental aspect
of these distributions is the study of the local maxima of the density, or
modes....

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

Journal of theoretical probability, ISSN 0894-9840, 6/2016, Volume 29, Issue 2, pp. 550 - 568

We prove the Lukacs–Olkin–Rubin theorem without invariance of the distribution of the “quotient,” which was the key assumption in the original proof of...

Riesz distribution | Symmetric cones | 62H05 | Functional equations | Wishart distribution | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Lukacs characterization | Division algorithm | Statistics & Probability | Physical Sciences | Science & Technology

Riesz distribution | Symmetric cones | 62H05 | Functional equations | Wishart distribution | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Lukacs characterization | Division algorithm | Statistics & Probability | Physical Sciences | Science & Technology

Journal Article

The Annals of statistics, ISSN 0090-5364, 10/2013, Volume 41, Issue 5, pp. 2700 - 2702

We report an error in Theorem 4.1 of the paper identified in the title. That theorem is not true in general. However, the main mathematical message in the...

Paper | Matrices | Mathematical theorems | Random variables | 60G46 | 62H05 | standardization | Normalization | 60F15

Paper | Matrices | Mathematical theorems | Random variables | 60G46 | 62H05 | standardization | Normalization | 60F15

Journal Article

The Annals of statistics, ISSN 0090-5364, 04/2000, Volume 28, Issue 2, pp. 461 - 482

Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several...

Datasets | Data Depth | Maximality | Infinity | Random sampling | Statistical theories | Inference | Mathematical functions | Convexity | Covariance matrices | Estimators | Halfspace depth | Simplicial depth | Statistical depth functions | Multivariate symmetry | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | 62H05 | 62G20 | halfspace depth | multivariate symmetry | simplicial depth

Datasets | Data Depth | Maximality | Infinity | Random sampling | Statistical theories | Inference | Mathematical functions | Convexity | Covariance matrices | Estimators | Halfspace depth | Simplicial depth | Statistical depth functions | Multivariate symmetry | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | 62H05 | 62G20 | halfspace depth | multivariate symmetry | simplicial depth

Journal Article

Dependence modeling, ISSN 2300-2298, 03/2018, Volume 6, Issue 1, pp. 47 - 62

Motivated by the nice characterization of copulas A for which d
(A, A
) is maximal as established independently by Nelsen [11] and Klement & Mesiar [7], we...

62H05 | exchangeability | Copula | symmetry | Markov kernel | 28A12 | 62E10 | complete dependence | 60E05

62H05 | exchangeability | Copula | symmetry | Markov kernel | 28A12 | 62E10 | complete dependence | 60E05

Journal Article

The Annals of statistics, ISSN 0090-5364, 4/2002, Volume 30, Issue 2, pp. 455 - 474

In many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors, and less concerned...

Dimensionality reduction | Objective functions | Linear regression | Matrices | Eigenvectors | Mathematical vectors | Regression analysis | Modeling | Nonparametric Function Estimation | Estimators | Estimation methods | Graphics | Visualization | Regression | Central subspace | SAVE | pHd | SIR | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | 62H05 | visualization | 62G08 | regression | 62-09 | graphics

Dimensionality reduction | Objective functions | Linear regression | Matrices | Eigenvectors | Mathematical vectors | Regression analysis | Modeling | Nonparametric Function Estimation | Estimators | Estimation methods | Graphics | Visualization | Regression | Central subspace | SAVE | pHd | SIR | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | 62H05 | visualization | 62G08 | regression | 62-09 | graphics

Journal Article

The Annals of statistics, ISSN 0090-5364, 8/2015, Volume 43, Issue 4, pp. 1647 - 1681

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and...

Structural estimation | Graphical models | Structural Markov laws | Hyper Markov laws | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Graph theory | Markov analysis | Comparative analysis | Bayesian analysis | Definitions | 62H05 | hyper Markov laws | 05C90 | structural Markov laws | structural estimation | 05C80 | 68T30

Structural estimation | Graphical models | Structural Markov laws | Hyper Markov laws | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Graph theory | Markov analysis | Comparative analysis | Bayesian analysis | Definitions | 62H05 | hyper Markov laws | 05C90 | structural Markov laws | structural estimation | 05C80 | 68T30

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2007, Volume 35, Issue 6, pp. 2654 - 2690

In this paper we propose two new methods to estimate the dimension-reduction directions of the central subspace (CS) by constructing a regression model such...

Dimensionality reduction | Preliminary estimates | Density estimation | Error rates | Eigenvalues | Automobiles | Pollutants | Estimators | Consistent estimators | Estimation methods | Conditional density function | Efficient dimension reduction | Convergence of algorithm | Root-n consistency | Double-kernel smoothing | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Statistical analysis | 62H05 | 62G08 | 62G09 | convergence of algorithm | double-kernel smoothing | root-n consistency | efficient dimension reduction

Dimensionality reduction | Preliminary estimates | Density estimation | Error rates | Eigenvalues | Automobiles | Pollutants | Estimators | Consistent estimators | Estimation methods | Conditional density function | Efficient dimension reduction | Convergence of algorithm | Root-n consistency | Double-kernel smoothing | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Statistical analysis | 62H05 | 62G08 | 62G09 | convergence of algorithm | double-kernel smoothing | root-n consistency | efficient dimension reduction

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 11/2015, Volume 288, pp. 159 - 168

Multivariate normal stable Tweedie models are recently introduced as an extension to normal gamma and normal inverse Gaussian models. The aim of this paper is...

Variance function | Symmetric matrix | Natural exponential family | Pseudo-orthogonality | 62E10 | MSC 62H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Computation | Mathematical analysis | Mathematical models | Gaussian | Polynomials | Inverse | Variance

Variance function | Symmetric matrix | Natural exponential family | Pseudo-orthogonality | 62E10 | MSC 62H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Computation | Mathematical analysis | Mathematical models | Gaussian | Polynomials | Inverse | Variance

Journal Article

The Annals of statistics, ISSN 0090-5364, 6/2012, Volume 40, Issue 3, pp. 1682 - 1713

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model...

Identifiability | Gaussian distributions | Algebra | Logical theorems | Polynomials | Structural equation models | Coefficients | Flow graphs | Covariance matrices | Vertices | Gaussian distribution | Graphical model | Multivariate normal distribution | Covariance matrix | Parameter identification | Structural equation model | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Models | Linear equations | Simulation | Normal distribution | 62H05 | 62J05 | graphical model | multivariate normal distribution | parameter identification | structural equation model

Identifiability | Gaussian distributions | Algebra | Logical theorems | Polynomials | Structural equation models | Coefficients | Flow graphs | Covariance matrices | Vertices | Gaussian distribution | Graphical model | Multivariate normal distribution | Covariance matrix | Parameter identification | Structural equation model | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Models | Linear equations | Simulation | Normal distribution | 62H05 | 62J05 | graphical model | multivariate normal distribution | parameter identification | structural equation model

Journal Article

Dependence modeling, ISSN 2300-2298, 07/2019, Volume 7, Issue 1, pp. 259 - 278

We show that any distribution function on ℝ
with nonnegative, nonzero and integrable marginal distributions can be characterized by a norm on ℝ
, called
-norm....

Characteristic function | 62H05 | 60G99 | multivariate distribution | 60E10 | empirical distribution function | Wasserstein metric | 62H12 | Hausdorff metric | norm | 62h05 | d-norm | wasserstein metric | hausdorff metric | 60e10 | 62h12 | characteristic function | 60g99

Characteristic function | 62H05 | 60G99 | multivariate distribution | 60E10 | empirical distribution function | Wasserstein metric | 62H12 | Hausdorff metric | norm | 62h05 | d-norm | wasserstein metric | hausdorff metric | 60e10 | 62h12 | characteristic function | 60g99

Journal Article

The Annals of statistics, ISSN 0090-5364, 8/2006, Volume 34, Issue 4, pp. 1814 - 1826

In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control...

Discriminants | Control groups | Gaussian distributions | Approximation | Canonical forms | Matching Methods for Observational Studies | Sampling bias | Cigarette smoking | Sampling distributions | Observational studies | Covariance matrices | Causal inference | Matched sampling | Equal percent bias reducing (EPBR) | Propensity scores | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Causality | Sampling | Statistics | 62H05 | 62H30 | equal percent bias reducing (EPBR) | propensity scores | matched sampling | 62D05 | 60E05 | 62K99

Discriminants | Control groups | Gaussian distributions | Approximation | Canonical forms | Matching Methods for Observational Studies | Sampling bias | Cigarette smoking | Sampling distributions | Observational studies | Covariance matrices | Causal inference | Matched sampling | Equal percent bias reducing (EPBR) | Propensity scores | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical models | Causality | Sampling | Statistics | 62H05 | 62H30 | equal percent bias reducing (EPBR) | propensity scores | matched sampling | 62D05 | 60E05 | 62K99

Journal Article

Sankhya B, ISSN 0976-8386, 6/2019, Volume 81, Issue 1, pp. 60 - 74

The family of Inverse Gaussian (IG) distributions has applications in areas such as hydrology, lifetime testing, and reliability, among others. In this paper,...

Characterizations | 62H15 | 62H05 | 62P30 | Goodness-of-fit test | Secondary 62F40 | Data transformations | Statistics, general | Shapiro-Wilk test | Statistics | Gamma distribution | Convolution | Anderson-Darling test | Primary 62F03 | 62F05

Characterizations | 62H15 | 62H05 | 62P30 | Goodness-of-fit test | Secondary 62F40 | Data transformations | Statistics, general | Shapiro-Wilk test | Statistics | Gamma distribution | Convolution | Anderson-Darling test | Primary 62F03 | 62F05

Journal Article

Test (Madrid, Spain), ISSN 1863-8260, 05/2018, Volume 28, Issue 2, pp. 475 - 498

In this paper, we define a new skewness ordering that enables stochastic comparisons for vectors that follow a multivariate skew-normal distribution. The new...

62H05 | Statistics for Business, Management, Economics, Finance, Insurance | Statistical Theory and Methods | Skew-normal distribution | Statistics, general | Statistics | Canonical transformation | Convex transform order | 60E05 | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Analysis | Management science | Numerical analysis | Skewed distributions | Divergence | Transformations (mathematics) | Normal distribution | Skewness | Multivariate analysis

62H05 | Statistics for Business, Management, Economics, Finance, Insurance | Statistical Theory and Methods | Skew-normal distribution | Statistics, general | Statistics | Canonical transformation | Convex transform order | 60E05 | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Analysis | Management science | Numerical analysis | Skewed distributions | Divergence | Transformations (mathematics) | Normal distribution | Skewness | Multivariate analysis

Journal Article

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